##### Question 1:

Describe how the following expressions are obtained:

4x^{2} – 5x, 7xy + 5, x^{2}y

##### Answer:

##### Question 2:

What are the terms in the following expressions? Show how the terms are formed. Draw a tree
diagram for each expression.

8y + 3x^{2}, 7mn – 4, 2x^{2}y.

##### Answer:

We can represent the terms and factors of the terms of an expression by a tree diagram

##### Question 3:

Write three expressions each having 4 terms.

##### Answer:

Three expressions each having 4 terms are:

(i) 4x^{2} – 3y^{2} + 9x – 8y

(ii) 4x^{2} – 3xy + 4x + 13

(iii) 5x^{3} – 5x^{2} – 5x – 5

##### Question 4:

Identify the coefficients in the following terms:

4x – 3y, a + b + 5, 2y + 5, 2xy.

##### Answer:

In 4x – 3y,

4 is the coefficient of x and – 3 is the coefficient
of y.

In a + b + 5

The coefficient of a and b is 1.

In 2y + 5, the coefficient of y is 2.

In 2xy, 2 is the coefficient of xy, x is the
coefficient of 2y and y is the coefficient of 2x.

##### Question 5:

Group the like terms together from the following:

12x, 12, –25x, –25, –25y, 1, x, 12y, y

##### Answer:

Like terms are:

(i) 12x, –25x, x

(ii) 12, –25, 1

(iii) –25y, 12y, y

##### Question 6:

Classify the following expressions as a monomial, a binomial or a trinomial:

a, a + b, ab + a + b, ab + a + b – 5, xy, xy + 5, 5x^{2} – x + 2, 4pq – 3q + 5p, 7,
4m – 7n + 10, 4mn + 7.

##### Answer:

Monomials: a, xy, 7

Binomials: a + b, xy + 5, 4mn + 7

Trinomials: ab + a + b, 5x^{2} – x + 2, 4m – 4n + 10,
4pq – 3q + 5p

##### Question 7:

Get the algebraic expression in the following cases using variables, constants and arithmatic
operations.

Subtraction of z from y.

##### Answer:

y – z

##### Question 8:

Get the algebraic expression in the following cases using variables, constants and arithmatic
operations.

One half of the sum of numbers x and y.

##### Answer:

##### Question 9:

Get the algebraic expression in the following cases using variables, constants and arithmatic
operations.

The number z multiplied by itself.

##### Answer:

z^{2}

##### Question 10:

Get the algebraic expression in the following cases using variables, constants and arithmatic
operations.

One fourth of the product of numbers p and q.

##### Answer:

##### Question 11:

Get the algebraic expression in the following cases using variables, constants and arithmatic
operations.

Numbers x and y both squared and added.

##### Answer:

x^{2} + y^{2}

##### Question 12:

Get the algebraic expression in the following cases using variables, constants and arithmatic
operations.

Number 5 added to three times the product of numbers m and n.

##### Answer:

3mn + 5

##### Question 13:

Get the algebraic expression in the following cases using variables, constants and arithmatic
operations.

Product of numbers y and z subtracted from 10.

##### Answer:

10 – yz

##### Question 14:

Get the algebraic expression in the following cases using variables, constants and arithmatic
operations.

Sum of numbers a and b subtracted from their product.

##### Answer:

ab – (a + b)

##### Question 15:

Identify the terms and their factors in the following expressions. Show the terms and factors
by tree diagrams.

x – 3

##### Answer:

##### Question 16:

Identify the terms and their factors in the following expressions. Show the terms and factors
by tree diagrams.

1 + x + x^{2}

##### Answer:

##### Question 17:

Identify the terms and their factors in the following expressions. Show the terms and factors
by tree diagrams.

y – y^{3}

##### Answer:

##### Question 18:

Identify the terms and their factors in the following expressions. Show the terms and factors
by tree diagrams.

5xy^{2} + 7x^{2}y

##### Answer:

##### Question 19:

Identify the terms and their factors in the following expressions. Show the terms and factors
by tree diagrams.

– ab + 2b^{2} – 3a^{2}

##### Answer:

##### Question 20:

##### Answer:

##### Question 21:

##### Answer:

##### Question 22:

##### Answer:

##### Question 23:

##### Answer:

##### Question 24:

##### Answer:

##### Question 25:

State whether a given pair of terms is of like or unlike terms:

1, 100

##### Answer:

1, 100 are like terms.

##### Question 26:

State whether a given pair of terms is of like or unlike terms:

##### Answer:

##### Question 27:

State whether a given pair of terms is of like or unlike terms:

– 29x, – 29y

##### Answer:

–29x, –29y are unlike terms.

##### Question 28:

State whether a given pair of terms is of like or unlike terms:

14xy, 42yx

##### Answer:

14xy, 42yx are like terms.

##### Question 29:

State whether a given pair of terms is of like or unlike terms:

4m^{2}p, 4mp^{2}

##### Answer:

4m^{2}p, 4mp^{2} are unlike terms.

##### Question 30:

State whether a given pair of terms is of like or unlike terms:

12xz, 12x^{2}z^{2}

##### Answer:

12xz, 12x^{2}z^{2} are unlike terms.

##### Question 31:

Identify like terms in the following:

##### Answer:

##### Question 32:

Identify like terms in the following:

##### Answer:

##### Question 33:

Think of at least two situations in which you need to form two algebraic expressions and add or subtract them.

##### Answer:

(i) The sides of a triangle are x cm, y cm and z cm respectively. Then the perimeter of the
triangle is x + y + z.

(ii) Out of a class of 50 students, x students failed, then the number of students passed =
50 – x.

##### Question 34:

Add and subtract:

m – n, m + n

##### Answer:

m – n + m + n = 2m

m – n – (m + n) = m – n – m – n = – 2n

##### Question 35:

Add and subtract:

mn + 5 – 2, mn + 3

##### Answer:

(mn + 5 – 2) + (mn + 3) = mn + 5 – 2 + mn + 3

= 2mn + 6

(mn + 5 – 2) – (mn + 3) = mn + 5 – 2 – mn – 3 = 0

##### Question 36:

Simplify combining like terms:

21b – 32 + 7b – 20b

##### Answer:

21b – 32 + 7b – 20b

= 21b + 7b – 20b – 32 = (21 + 7 – 20) b – 32

= 8b – 32

##### Question 37:

Simplify combining like terms:

–z^{2} + 13z^{2} – 5z + 7z^{3} – 15z

##### Answer:

##### Question 38:

Simplify combining like terms:

p – (p – q) – q – (q – p)

##### Answer:

p – (p – q) – q – (q – p) = p – p + q – q – q + p

= p – p + p + q – q – q = p – q

##### Question 39:

Simplify combining like terms:

3a – 2b – ab – (a – b + ab) + 3ab + b – a

##### Answer:

3a – 2b – ab – (a – b + ab) + 3ab + b – a

= 3a – 2b – ab – a + b – ab + 3ab + b – a

= 3a – a – a – 2b + b + b – ab – ab + 3ab

= a + ab

##### Question 40:

Simplify combining like terms:

##### Answer:

##### Question 41:

Simplify combining like terms:

(3y^{2} + 5y^{2} – 4) – (8y – y^{2} – 4)

##### Answer:

##### Question 42:

Add:

3mn, – 5mn, 8mn, – 4mn

##### Answer:

(3mn) + (–5mn) + (8mn) + (–4mn)

= 3mn – 5mn + 8mn – 4mn

= 3mn + 8mn – 5mn – 4mn

= 11mn – 9mn = 2mn

##### Question 43:

Add:

t – 8tz, 3tz – z, z – t

##### Answer:

t – 8tz + 3tz – z + z – t

= t – t – 8tz + 3tz – z + z

= –5tz

##### Question 44:

Add:

–7mn + 5, 12mn + 2, 9mn – 8, – 2mn – 3

##### Answer:

(–7mn + 5) + (12mn + 2) + (9mn – 8) +

(–2mn – 3)

= –7mn + 5 + 12mn + 2 + 9mn – 8 – 2mn – 3

= –7mn + 12mn + 9mn – 2mn + 5 + 2 – 8 – 3

= 21mn – 9mn + 7 – 11 = 12mn – 4

##### Question 45:

Add:

a + b – 3, b – a + 3, a – b + 3

##### Answer:

(a + b – 3) + (b – a + 3) + (a – b + 3)

= a + b – 3 + b – a + 3 + a – b + 3

= a + b + b – a + a – b – 3 + 3 +3

= a + b + 3

##### Question 46:

Add:

14x + 10y – 12xy – 13, 18 – 7x – 10y

+ 8xy, 4xy

##### Answer:

(14x + 10y – 12xy – 13) +

(18 – 7x – 10y + 8xy) + 4xy

= 14x + 10y – 12xy – 13 + 18 – 7x – 10y + 8xy + 4xy

= (14 – 7)x + (10 – 10) y + (– 12 + 8 + 4) xy

+ (– 13 + 18) = 7x + 5

##### Question 47:

Add:

5m – 7n, 3n – 4m + 2, 2m – 3mn – 5

##### Answer:

(5m – 7n) + (3n – 4m + 2) + (2m – 3mn – 5)

= 5m – 7n + 3n – 4m + 2 + 2m – 3mn – 5

= 5m + 2m – 4m – 7n + 3n + 2 – 5 – 3mn

= 3m – 4n – 3 – 3mn

##### Question 48:

Add:

##### Answer:

##### Question 49:

Add:

##### Answer:

##### Question 50:

Add:

ab – 4a, 4b – ab, 4a – 4b

##### Answer:

(ab – 4a) + (4b – ab) + (4a – 4b)

= ab – 4a + 4b – ab + 4a – 4b

= ab – ab – 4a + 4a + 4b – 4b = 0

##### Question 51:

Add:

##### Answer:

##### Question 52:

Subtract:

–5y^{2} from y^{2}

##### Answer:

##### Question 53:

Subtract:

6xy from – 12xy

##### Answer:

– 12xy – 6xy

= – 18xy

##### Question 54:

Subtract:

(a – b) from (a + b)

##### Answer:

(a + b) – (a – b)

= a + b – a + b = 2b

##### Question 55:

Subtract:

a(b – 5) from b(5 – a)

##### Answer:

b (5 – a) – a(b – 5)

= 5b – ab – ab + 5a

= 5a + 5b – 2ab

##### Question 56:

Subtract:

–m^{2} + 5mn from 4m^{2} – 3mn + 8

##### Answer:

##### Question 57:

Subtract:

–x^{2} + 10x – 5 from 5x – 10

##### Answer:

##### Question 58:

Subtract:

##### Answer:

##### Question 59:

Subtract:

##### Answer:

##### Question 60:

What should be added to x^{2} + xy + y^{2} to obtain 2x^{2} + 3xy?

##### Answer:

##### Question 61:

What should be subtracted from 2a + 8b + 10 to get – 3a + 7b + 16?

##### Answer:

##### Question 62:

##### Answer:

##### Question 63:

From the sum of 3x – y + 11 and – y – 11 subtract 3x – y – 11.

##### Answer:

##### Question 64:

##### Answer:

##### Question 65:

If m = 2, find the value of

m – 2

##### Answer:

The value of (m – 2), when m = 2, is 0.

##### Question 66:

If m = 2, find the value of

3m – 5

##### Answer:

Put the value m = 2 in 3m – 5,

∴ 3m – 5 = 3 (2) – 5 = 6 – 5 = 1

The value of (3m – 5), when m = 2, is 1.

##### Question 67:

If m = 2, find the value of

9 – 5m

##### Answer:

Put the value m = 2 in 9 – 5m,

∴ 9 – 5m = 9 – (5 × 2)

= 9 – 10 = – 1

The value of (9 – 5m), when m = 2, is – 1.

##### Question 68:

If m = 2, find the value of

3m^{2} – 2m – 7

##### Answer:

##### Question 69:

##### Answer:

##### Question 70:

If p = – 2, find the value of

4p + 7

##### Answer:

Put p = (–2) in 4p + 7,

∴ 4p + 7 = 4 × (– 2) + 7 = – 8 + 7 = – 1

The value of (4p + 7), when p = –2, is –1.

##### Question 71:

If p = – 2, find the value of

–3p^{2} + 4p + 7

##### Answer:

##### Question 72:

If p = – 2, find the value of

–2p^{3} – 3p^{2} + 4p + 7

##### Answer:

##### Question 73:

Find the value of the following expression,
when x = –1.

2x – 7

##### Answer:

Put x = –1 in 2x – 7,

2x – 7 = 2 (–1) – 7 = –2 – 7 = –9

∴ The value of (2x – 7), when x = –1, is –9.

##### Question 74:

Find the value of the following expression,
when x = –1.

–x + 2

##### Answer:

Put x = –1 in –x + 2,

–x + 2 = –(–1) + 2 = 1 + 2 = 3

The value of (–x + 2), when x = –1, is 3.

##### Question 75:

Find the value of the following expression,
when x = –1.

x^{2} + 2x + 1

##### Answer:

Put x = –1 in x^{2} + 2x + 1

x^{2} + 2x + 1 = (–1)^{2} + 2 (–1) + 1 = 1 – 2 + 1

= 2 – 2 = 0

The value of (x^{2} + 2x + 1), when x = –1, is 0.

##### Question 76:

Find the value of the following expression,
when x = –1.

2x^{2} – x – 2

##### Answer:

Put x = –1, in 2x^{2} – x – 2.

2x^{2} – x – 2 = 2 (–1)^{2} –(–1) – 2

= 2 × 1 + 1 – 2 = 2 + 1 – 2 = 3 – 2 = 1

The value of (2x^{2} – x – 2), when x = –1, is 1.

##### Question 77:

If a = 2, b = –2, find the value of:

a^{2} + b^{2}

##### Answer:

##### Question 78:

If a = 2, b = –2, find the value of:

a^{2} + ab + b^{2}

##### Answer:

##### Question 79:

If a = 2, b = –2, find the value of:

a^{2} – b^{2}

##### Answer:

##### Question 80:

When a = 0, b = –1, find the value of the given
expressions:

2a + 2b

##### Answer:

Substituting a = 0, b = –1, in 2a + 2b,
2a + 2b = 2 (0) + 2 (–1)

= 0 – 2 = –2

∴ 2a + 2b = –2, when a = 0, b = –2.

##### Question 81:

When a = 0, b = –1, find the value of the given
expressions:

2a^{2} + b^{2} + 1

##### Answer:

##### Question 82:

When a = 0, b = –1, find the value of the given
expressions:

2a^{2}b + 2ab^{2} + ab

##### Answer:

##### Question 83:

When a = 0, b = –1, find the value of the given
expressions:

a^{2} + ab + 2.

##### Answer:

##### Question 84:

Simplify the expressions and find the value
if x is equal to 2.

x + 7 + 4 (x – 5)

##### Answer:

Put x = 2 in the given expression,
x + 7 + 4 (x – 5) = x + 7 + 4x – 20

= 5x – 13

= 5 (2) – 13 = 10 – 13 = –3

∴ x + 7 + 4 (x – 5) = –3, when x = 2.

##### Question 85:

Simplify the expressions and find the value
if x is equal to 2.

3 (x + 2) + 5x – 7

##### Answer:

Put x = 2 in the given expression

3 (x + 2) + 5x – 7 = 3x + 6 + 5x – 7

= 8x – 1

= 8 × 2 – 1

= 16 – 1 = 15

∴ 3 (x + 2) + 5x – 7 = 15, when x = 2.

##### Question 86:

Simplify the expressions and find the value
if x is equal to 2.

6x + 5 (x – 2)

##### Answer:

Put x = 2 in the given expression.

6x + 5 (x – 2) = 6x + 5x – 10

= 11x – 10

= 11 (2) – 10 = 22 – 10 = 12

∴ 6x + 5 (x – 2) = 12, when x = 2.

##### Question 87:

Simplify the expressions and find the value
if x is equal to 2.

4 (2x – 1) + 3x + 11

##### Answer:

Put x = 2 in the given expression.

4 (2x – 1) + 3x + 11 = 8x – 4 + 3x + 11

= 11x + 7

= 11 × 2 + 7 = 22 + 7 = 29

∴ 4 (2x – 1) + 3x + 11 = 29, when x = 2.

##### Question 88:

Simplify these expressions and find their
value if x = 3, a = –1, b = –2.

3x – 5 – x + 9

##### Answer:

3x – 5 – x + 9 = 3x – x – 5 + 9 = 2x + 4

Now, put x = 3 in 2x + 4,

2x + 4 = 2 × 3 + 4 = 6 + 4 = 10

∴ 3x – 5 – x + 9 = 10, when x = 3.

##### Question 89:

Simplify these expressions and find their
value if x = 3, a = –1, b = –2.

2 – 8x + 4x + 4

##### Answer:

2 – 8x + 4x + 4 = 2 + 4 – 8x + 4x

= 6 – 4x

Now, put x = 3 in 6 – 4x

6 – 4x = 6 – 4 × 3 = 6 – 12 = –6

∴ 2 – 8x + 4x + 4 = – 6, when x = 3.

##### Question 90:

Simplify these expressions and find their
value if x = 3, a = –1, b = –2.

3a + 5 – 8a + 1

##### Answer:

3a + 5 – 8a + 1 = 3a – 8a + 5 + 1

= –5a + 6

Now, put a = – 1 in – 5a + 6,

– 5a + 6 = – 5 (– 1) + 6 = 5 + 6 = 11

∴ 3a + 5 – 8a + 1 = 11, when a = – 1.

##### Question 91:

Simplify these expressions and find their
value if x = 3, a = –1, b = –2.

10 – 3b – 4 – 5b

##### Answer:

10 – 3b – 4 – 5b = 10 – 4 – 3b – 5b = 6 – 8b

Now, put b = –2 in 6 – 8b

6 – 8b = 6 – 8 × (–2) = 6 + 16 = 22

∴ 10 – 3b – 4 – 5b = 22, when b = –2.

##### Question 92:

Simplify these expressions and find their
value if x = 3, a = –1, b = –2.

2a – 2b – 4 – 5 + a

##### Answer:

2a – 2 b – 4 – 5 + a = 2 a + a – 2 b – 4 – 5

= 3a – 2b – 9

Now, put a = –1, b = –2 in 3a – 2b – 9,

3a – 2b – 9 = 3 (– 1) – 2 (–2) – 9 = – 3 + 4 – 9

= –12 + 4 = –8

∴ 2a – 2b – 4 – 5 + a = – 8, when a = –1, b = –2.

##### Question 93:

If z = 10, find the value of z^{3} – 3 (z – 10).

##### Answer:

##### Question 94:

If p = –10, find the value of p^{2} – 2p – 100.

##### Answer:

##### Question 95:

What should be the value of a if the value
of 2x^{2} + x – a equals to 5, when x = 0 ?

##### Answer:

Here, 2x^{2} + x – a = 5

Putting x = 0, we get

2 (0)^{2} + (0) – a = 5

–a = 5

∴ a = –5

##### Question 96:

Simplify the expression and find its value
when a = 5 and b = –3.

2 (a^{2} + ab) + 3 – ab.

##### Answer:

##### Question 97:

##### Answer:

##### Question 98:

Use the given algebraic expression to complete the table of number patterns (sequences).