Question

Factorize the following expressions:

`8x^2y^3 - x^5`

Answer 1

`=x^2(8y^3 - x^3)`

`= x^2((2y)^3 - x^3)`

`= x^2(2y - x)((2y)^2 + 2y(x) + x^2)     [∵ a^3 - b^3 = (a - b)(a^2 + ab + b^2)]`

`= x^2(2y - x)((2y)^2 + 2y(x)+ x^2)`      `[∵ a^3 - b^3 = (a - b)(a^2 + ab + b^2)]`

`= x^2(2y - x)(4y^2 + 2xy + x^2)`

`∴ 8x^2y^3 - x^5 = x^2(2y - x)(4y^2 + 2xy + x^2)`