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Question

Evaluate:
$$ (a^{2}+b^{2})(a+b)(a-b)$$, using the result of $$(a+b)(a-b)$$


Solution

$$ (a^{2}+b^{2})(a+b)(a-b)$$
We know that $$(a+b)(a-b)=a^2-b^2$$
So,
Substituting the result we get $$=(a^{2}+b^{2})$$ $$(a^{2}-b^{2})$$
It can be written as $$=a^{2}(a^{2}-b^{2})$$ + $$b^{2}(a^{2}-b^{2})$$
So we get  $$=a^{4}-a^{2}b^{2}+a^{2}b^{2}-b^{4}$$
$$=a^{4}-b^{4}$$

Mathematics

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