Question

(a⁴+b⁴)(a⁸-a⁴b⁴+b⁸) factorisation​

Answer 1

Explanation:

Let a^4 be x and b^4 be y.

$(a^4 + b^4)(a^8 - a^4b^4 + b^8)$

$= (x + y)(x^2 - xy + y^2)$ [substituting the values]

$= (x+y)(x^2 + 2xy + y^2 - 3xy)$

$=(x+y)[(x+y)^2 - 3xy]$

$= (x+y)^3 -3xy(x+y)$

$= x^3 + y^3$

$= (a^4)^3 + (b^4)^3$

$= a^12 + b^12$

Answer: a^12 + b^12