Factorise the following
a. b square m + b square n
b. 54x square y + 24 xy
c. 6ab +6bc
Answers
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)