Advertisements
Advertisements
Question
Factorise the following using the identity a2 – b2 = (a + b)(a – b).
a4 – (a – b)4
Advertisements
Solution
We have,
a4 – (a – b)4 = (a2)2 – [(a – b)2]2
= [a2 + (a – b)2][a2 – (a – b)2]
= [a2 + a2 + b2 – 2ab][a2 – (a2 + b2 – 2ab)]
= [2a2 + b2 – 2ab][–b2 + 2ab]
= (2a2 + b2 – 2ab)(2ab – b2)
APPEARS IN
RELATED QUESTIONS
The product of (x + 5) and (x – 5) is ____________
(7x + 3)(7x – 4) = 49x2 – 7x – 12
Factorise the following algebraic expression by using the identity a2 – b2 = (a + b)(a – b)
z2 – 16
Factorise the following using the identity a2 – b2 = (a + b)(a – b).
`x^2/9 - y^2/25`
Factorise the following using the identity a2 – b2 = (a + b)(a – b).
`(4x^2)/9 - (9y^2)/16`
Factorise the following using the identity a2 – b2 = (a + b)(a – b).
(x + y)4 – (x – y)4
Factorise the following using the identity a2 – b2 = (a + b)(a – b).
9x2 – (3y + z)2
Factorise the expression and divide them as directed:
(x4 – 16) ÷ x3 + 2x2 + 4x + 8
Verify the following:
(ab + bc)(ab – bc) + (bc + ca)(bc – ca) + (ca + ab)(ca – ab) = 0
Verify the following:
(a2 – b2)(a2 + b2) + (b2 – c2)(b2 + c2) + (c2 – a2) + (c2 + a2) = 0
