Question 92 (xviii)

Factorise the following using the identity $a^{2} - b^{2} = (a + b) (a - b) .$

$a^{4} - (a - b)^{4}$

Open in App

Solution

$a^{4} - (a - b)^{4} = (a^{2})^{2} - [(a - b)^{2}]^{2} = [a^{2} + (a - b)^{2}] [a^{2} - (a - b)^{2}] = [a^{2} + a^{2} + b^{2} - 2 a b] [a^{2} - (a^{2} + b^{2} - 2 a b)] = [2 a^{2} + b^{2} - 2 a b] [- b^{2} + 2 a b] = (2 a^{2} + b^{2} - 2 a b) (2 a b - b^{2})$

Suggest Corrections

Similar questions

Question 92 (xxvi)

Factorise the following using the identity $a^{2} - b^{2} = (a + b) (a - b) .$

$(a - b)^{2} - (b - c)^{2}$

Question 92 (v)

Factorise the following using the identity $a^{2} - b^{2} = (a + b) (a - b) .$

$28 a y^{2} - 175 a x^{2}$

Question 92 (xxv)

Factorise the following using the identity $a^{2} - b^{2} = (a + b) (a - b) .$

$16 x^{4} - 625 y^{4}$

Question 92 (xxiii)

Factorise the following using the identity $a^{2} - b^{2} = (a + b) (a - b) .$

$x^{4} - y^{4}$

Question 92 (xix)

Factorise the following using the identity $a^{2} - b^{2} = (a + b) (a - b) .$

$x^{4} - 1$

Explore more