Factorize: @^ \begin{aligned} p^3 + q^3 + p + | Math Question and Answer | Edugain UAE

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Factorize: $\begin{aligned} p^3 + q^3 + p + q \end{aligned}$

Answer:

$( p + q ) ( p^2 - pq + q^2 + 1 )$

Step by Step Explanation:

We know that $(a^3 + b^3) = (a + b) (a^2 - ab + b^2)$ Thus $\begin{aligned} p^3 + q^3 + p + q = \space& ( p^3 + q^3 ) + ( p + q ) \\ = \space& ( p + q ) ( p^2 - pq + q^2) + ( p + q ) \\ = \space& ( p + q ) ( p^2 - pq + q^2 + 1 ) \end{aligned}$
Hence, $p^3 + q^3 + p + q = ( p + q ) ( p^2 - pq + q^2 + 1 ).$

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