Step-by-step explanation:

Factoring Polynomials Examples - Examples

Question 1 :

Factorise the following expressions:

(i) 2a2 + 4a2 b + 8a2 c

Solution :

= 2a2 + 4a2 b + 8a2 c

By factoring 2a from the three terms, we get

= 2a (a + 2ab + 4ac)

(ii) ab - ac - MB + mc

Solution :

= ab - ac - mb + mc

= a(b - c) - m(b - c)

= (a - m) (b - c)

Question 2 :

Factorise the following:

(i) x2 + 4x + 4

Solution :

= x2 + 4x + 4

= x2 + 2 ⋅ x ⋅ 2 + 22

= (x + 2)2

(ii) 3a2 - 24ab + 48b2

Solution :

= 3a2 - 24ab + 48b2

= 3 (A2 - 8ab + 16b2)

= 3 [a2 - 2a(4b) + (4b)2]

= 3 (a - 4b)2

(iii) x5 - 16x

Solution :

= x5 - 16x

= x(x4 - 16)

= x [(x2)2 - 42]

= x(x2 + 4)(x2 - 4)

= x(x2 + 4)(x + 2)(x - 2)

(iv) m2 + 1/m2 - 23

Solution :

m2 + 1/m2 - 23 = m2 + 1/m2 - 25 + 2

= (m2 + 1/m2 + 2) - 25

= (m + (1/m))2 - 52

= (m + (1/m) + 5) (m + (1/m) - 5)

(v) 6 - 216 x2

Solution :

= 6 - 216 x2

= 6(1 - 36x2)

= 6[1 - (6X)2]

= 6(1 + 6x)(1 - 6x)

(vi) a2 + 1/a2 - 18

Solution :

a2 + 1/a2 - 18 = a2 + 1/a2 - 16 - 2

= (a2 + 1/a2 - 2) - 16

= (a - (1/a))2 - 42

= (a + (1/a) + 4) (a + (1/a) - 4)