Question
Find the following products:
$\left(7 p^4+q\right)\left(49 p^8-7 p^4 q+q^2\right)$
$\left(7 p^4+q\right)\left(49 p^8-7 p^4 q+q^2\right)$
✓
Answer
we have,
$\left(7 p^4+q\right)\left(49 p^8-7 p^4 q+q^2\right)$
$=\left(7 p^4+q\right)\left[\left(7 p^4\right)^2-7 p^4 \times q+(q)^2\right]$
$=\left(7 p^4\right)^3+(q)^3\left[\because a^3+b^3=(a+b)\left(a^2-a b+b^2\right)\right]$
$=343 p^{12}+q^3$
$\therefore\left(7 p^4+q\right)\left(49 p^8-7 p^4 q+q^2\right)=343 p^{12}+q^3$
$\left(7 p^4+q\right)\left(49 p^8-7 p^4 q+q^2\right)$
$=\left(7 p^4+q\right)\left[\left(7 p^4\right)^2-7 p^4 \times q+(q)^2\right]$
$=\left(7 p^4\right)^3+(q)^3\left[\because a^3+b^3=(a+b)\left(a^2-a b+b^2\right)\right]$
$=343 p^{12}+q^3$
$\therefore\left(7 p^4+q\right)\left(49 p^8-7 p^4 q+q^2\right)=343 p^{12}+q^3$
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