Question

Find the continued product: $\left(x-3\right)\left(x+3\right)\left(x^2+9\right)$.

Answer 1

Calculate the required product

A continued product is the product of three or more terms.

Given, $\left(x-3\right)\left(x+3\right)\left(x^2+9\right)$

Simplifying,

$\begin{array}{cc}\left(x-3\right)\left(x+3\right)\left(x^2+9\right)=\left(x^2-3^2\right)\left(x^2+9\right)& \left[\because \left(a+b\right)\left(a-b\right)=a^2-b^2\right]\\ =\left(x^2-9\right)\left(x^2+9\right)& \\ ={\left(x^2\right)}^2-9^2& \\ =x^4-81& \end{array}$

Hence, the continued product $\left(x-3\right)\left(x+3\right)\left(x^2+9\right)$ is $x^4-81$.