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, $(7 p^{4}+q)(49 p^{8}-7 p^{4} q+q^{2})=343 p^{12}+q^{3}$.

Tutorialspoint

Updated on: 10-Oct-2022

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