Question

Factorise: $a^4-343a$

Answer 1

Factorisation Using Algebraic Identities

Given the expression $a^4-343a$,

$$\begin{gathered} a^4-343a=a(a^3-343) \\ =a\left(a^3-{\left(7\right)}^3\right) \\ =a\left(a-7\right)(a^2+a(7)+7^2)[\because a^3-b^3=(a-b\left)\right(a^2+ab+b^2)] \\ =a\left(a-7\right)(a^2+7a+49) \end{gathered}$$

Hence, $a^4-343a=a\left(a-7\right)(a^2+7a+49)$.