Question

Choose the appropriate pattern and use it to find the product: (p4−q4)(p4+q4).

Answer 1

The expression can be solved by expanding the bracket and multiplying out the terms

$(p^4-q^4)(p^4+q^4)$$\begin{gathered} =p^4(p^4+q^4)-q^4(p^4+q^4) \\ =p^8+p^4q^4-p^4q^4-q^8 \\ =p^8-q^8 \end{gathered}$

Therefore, the expression can be simplified as;

$p^8-q^8$

Alternatively, using the theorem of difference of two squares, which is

$a^2-b^2=(a-b)(a+b)$

Hence,

$p^8-q^8=(p^4)^2-(q^4)^2$