Find the common factors of the given terms.

.

Q 2.Factorise the following expressions.

Q 3.

Factorise.

(i) x^{2} + xy + 8x + 8y

(ii) 15xy – 6x + 5y – 2

(iii) ax + bx – ay – by

(iv) 15pq + 15 + 9q + 25p

(v) z – 7 + 7xy – xyz.

Q 4.

Factorise the following expressions.

Q 5.

Factorise

Q 6.

Factorise the expressions.

Q 7.

Factorise.

Q 8.

Factorise the following expressions.

(i) p^{2} + 6p + 8

(ii) q^{2} – 10q + 21

(iii) p^{2} + 6p – 16.

Q 9.

Carry out the following divisions.

Q 10.

Divide the given polynomials by the given monomial.

Q 11.

Work out the following divisions.

Q 12.

Divide as directed.

Q 13.

Factorise the expressions and divide them as directed.

Q 14.

Find and correct the errors in the following mathematical statements.

4(x – 5) = 4x – 5

The given statement is incorrect

The correct statement is 4(x – 5) = 4x – 20.

x(3x + 2) = 3x^{2} + 2

The given statement is incorrect.

The correct statement is x(3x + 2) = 3x^{2} + 2x.

2x + 3y = 5xy

SOLUTION:The given statement is incorrect.

The correct statement is 2x + 3y = 2x + 3y.

x + 2x + 3x = 5x

SOLUTION:The given statement is incorrect.

The correct statement is x + 2x + 3x = 6x.

5y + 2y + y – 7y = 0

SOLUTION:The given statement is incorrect.

The correct statement is 5y + 2y + y – 7y = y.

3x + 2x = 5x^{2}

The given statement is incorrect.

The correct statement is 3x + 2x = 5x.

(2x)^{2} + 4(2x) + 7 = 2x^{2} + 8x + 7

The given statement is incorrect.

The correct statement is (2x)^{2} + 4(2x) + 7

= 4x^{2} + 8x + 7.

(2x)^{2} + 5x = 4x + 5x = 9x

The given statement is incorrect.

The correct statement is (2x)^{2} + 5x = 4x^{2} + 5x.

(3x + 2)^{2} = 3x^{2} + 6x + 4

The given statement is incorrect.

The correct statement is (3x + 2)^{2}
= (3x)^{2} + 2(3x)(2) + 2^{2} = 9x^{2} + 12x + 4.

Substituting x = –3 in

Q 24.

(y – 3)^{2} = y^{2} – 9

Q 25.

(z + 5)^{2} = z^{2} + 25

Q 26.

(2a + 3b) (a – b) = 2a^{2} – 3b^{2}

Q 27.

(a + 4) (a + 2) = a^{2} + 8

Q 28.

(a – 4) (a – 2) = a2 – 8

SOLUTION:Q 29.

SOLUTION:

Q 30.

SOLUTION:

Q 31.

SOLUTION:

Q 32.

SOLUTION:

Q 33.

SOLUTION:

Q 34.

SOLUTION: