Advertisements
Advertisements
Question
Factorise the following algebraic expression by using the identity a2 – b2 = (a + b)(a – b)
x4 – y4
Advertisements
Solution
Let x4 – y4 = (x2)2 – (y2)2
We have a2 – b2 = (a + b)(a – b)
(x2)2 – (y2)2 = (x2 + y2)(x2 – y2)
x4 – y4 = (x2 + y2)(x2 – y2)
Again we have x2 – y2 = (x + y)(x – y)
∴ x4 – y4 = (x2 + y2)(x + y)(x – y)
APPEARS IN
RELATED QUESTIONS
Using the identity (a + b)(a – b) = a2 – b2, find the following product
(4 – mn)(mn + 4)
Evaluate the following, using suitable identity
990 × 1010
Factorise the following algebraic expression by using the identity a2 – b2 = (a + b)(a – b)
z2 – 16
Simplify (5x – 3y)2 – (5x + 3y)2
Factorise the following using the identity a2 – b2 = (a + b)(a – b).
`(2p^2)/25 - 32q^2`
Factorise the following using the identity a2 – b2 = (a + b)(a – b).
a4 – (a – b)4
Factorise the expression and divide them as directed:
(x2 – 22x + 117) ÷ (x – 13)
Factorise the expression and divide them as directed:
(2x3 – 12x2 + 16x) ÷ (x – 2)(x – 4)
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
