**Factorisation**

**Question 1.****Find the common factors of the given terms :(i)** 12x, 36

**(ii)**2y, 22xy

**(iii)**14pqr, 28p

^{2}q

^{2}

**(iv)**2x, 3x

^{2}, 4

**(v)**6abc, 24ab

^{2},12a

^{2}b

**(vi)**16x

^{3}, – 4x

^{2}, 32x

**(vii)**10pq, 20qr, 30rp

**(viii)**3x

^{2}y

^{3}, 10x

^{3}y

^{2}, 6x

^{2}y

^{2}z

**Solution:****(i)** The numerical coefficients in the given monomials are 12 and 36.

The highest common factor of 12 and 36 is 12.

But there is no common literal appearing in the given monomials 12x and 36.

∴ The highest common factor =12

**(ii)** The numerical coefficients of the given monomials are 2 and 22.

The highest common factor of 2 and 22 is 2.

The common literal appearing in the given monomials is y.

The smallest power of y in the two monomials =1

The monomial of common literals with smallest powers = y

∴ The highest common factor = 2y

**(iii)** The numerical coefficients of the given monomials are 14 and 28.

The highest common factor of 14 and 28 is 14.

The common literals appearing in the given monomials are p and q.

The smallest power of p and q in the two monomials = 1

The monomial of common literals with smallest powers pq

∴ The highest common factor = 14pq

**(iv)** The numerical coefficients of the given monomials are 2, 3, and 4.

The highest common factor of 2, 3 and 4 is 1.

There is no common literal appearing in the three monomials.

The highest common factor = 1

**(v)** The numerical coefficients of the given monomials are 6, 24 and 12.

The highest common factor of 6, 24 and 12 is 6.

The common literals appearing in the three monomials are a and b.

The smallest power of a in the three monomials = 1

The smallest power of b in the three monomials 1

The monomials of common literals with smallest powers = ab

Hence, the highest common factor =6 ab

**(vi)** The numerical coefficients of the given monomials are 16, 4 and 32.

The highest common factor of 16, 4 and 32 is 4.

The common literal appearing in the three monomials is x.

The smallest power of x in the three monomials =1

The monomial of common literal with smallest power = x

Hence, the highest common factor = 4x

**(vii)** The numerical coefficients of the given monomials are 10,20 and 30.

The highest common factor of 10, 20 and 30 is 10

There is no common literal appearing in the three monomials.

Hence, the highest common factors =10.

**(viii)** The numerical coefficients of the given monomials are 3, 10 and 6.

The highest common factor of 3, 10 and 6 is 1.

The common literals appearing in the three monomials are x and y.

The smallest power of x in the three monomials = 2

The smallest power of y in the three monomials = 2

The monomial of common literals with smallest powers = x^{2}y^{2}

Hence, the highest common factor = x^{2}y^{2}

**Question 2.****Factorise the following expressions****(i)** 7x – 42**(ii)** 6p – 12q**(iii)** 7a^{2} + 14a**(iv)** -16z + 20z^{2}**(v)** 20l^{2} m + 30alm**(vi)** 5x^{2}y – 15xy^{2}**(vii)** 10a^{2} + 15b^{2} + 20c^{2}**(viii)** -4a^{2} + 4ab – 4ca**(ix)** x^{2}yz + xy^{2}z + xyz^{2}**(x)** ax^{2}y + bxy^{2} + cxyz

**Solution:**

**Question 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

**Solution:**