Question

Factoring with repeated of the difference of square formula. Factor the answer completely. u⁴x³ – 81x³.

Answer 1

Given:

The expression u⁴x³ – 81x³.

Required:

Factoring with repeated of the difference of square formula.

Step-by-step explanation:

We will factor as:

`\begin{gathered} =u^4x^3-81x^3 \\ \text{ Take }x^3\text{ common} \\ =x^3(u^4-81) \\ \text{ we can also write it as} \\ =x^3((u^2)^2-9^2) \\ \text{ Use }a^2-b^2=(a-b)(a+b) \\ =x^3(u^2-9)(u^2+9) \\ =x^3(u^2-3^2)(u^2+9) \\ =x^3(u-3)(u+3)(u^2+9) \end{gathered}`

Answer:

`\text{ factor looks like }x^3(u-3)(u+3)(u^2+9).`