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Find the following products:
$(7p^4 + q) (49p^8 - 7p^4q + q^2)$
Given:
$(7p^4 + q) (49p^8 - 7p^4q + q^2)$
To do:
We have to find the given product.
Solution:
We know that,
$a^{3}+b^{3}=(a+b)(a^{2}-a b+b^{2})$
$a^{3}-b^{3}=(a-b)(a^{2}+a b+b^{2})$
Therefore,
$(7 p^{4}+q)(49 p^{8}-7 p^{4} q+q^{2})=(7 p^{4}+q)[(7 p^{4})^{2}-7 p^{4} \times q+(q)^{2}]$
$=(7 p^{4})^{3}+(q)^{3}$
$=343 p^{12}+q^{3}$
Hence, $(7 p^{4}+q)(49 p^{8}-7 p^{4} q+q^{2})=343 p^{12}+q^{3}$.
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