Advertisements
Advertisements
Question
Factorise:
(a2 - 1) (b2 - 1) + 4ab
Sum
Solution
(a2 - 1) (b2 - 1) + 4ab
= a2b2 - a2 - b2 + 1 + 4ab
= a2b2 + 1 + 2ab - a2 - b2 + 2ab
= (a2b2 + 1 + 2ab) - (a2 + b2 - 2ab)
= (ab + 1)2 - (a - b)2
= [(ab + 1) - (a - b)][(ab + 1) + (a - b)] ...[∵ a2 - b2 = (a + b)(a - b)]
= [ab + 1 - a + b][ab + 1 + a - b]
shaalaa.com
Method of Factorisation : Difference of Two Squares
Is there an error in this question or solution?
APPEARS IN
RELATED QUESTIONS
Factorise : a2 - (2a + 3b)2
Factorise : 4a2b - 9b3
Factorise : a4 - 1
Factorise : 4x2 - 12ax - y2 - z2 - 2yz + 9a2
Factorise : `4x^2 + 1/(4x)^2 + 1`
Factorise the following by the difference of two squares:
(x + y)2 -1
Factorise the following by the difference of two squares:
(x - 2y)2 -z2
Factorise the following:
(x + y)3 - x - y
Factorise the following:
y4 + y2 + 1
Factorise the following:
(a2 - b2)(c2 - d2) - 4abcd
