Question

Evaluate:
$(a+b)(a-b)(a^2+b^2)$ is $a^4-b^4$.
If true, then enter $1$ and if false, then enter $0$.

Answer 1

Given, $(a+b)(a-b)(a^2+b^2)$.

We know, $(a+b)(a-b)$ $=(a^2-b^2)$.

Multiply by using direct method, we get,
$(a+b)(a-b)(a^2+b^2)=[a^2-b^2](a^2+b^2)$
$=(a^2+b^2)(a^2-b^2)$.

Now, by using formula $(a^2-b^2)=(a+b)(a-b)$, we get,

$=\left(\right(a^2{)}^2-\left(b^2{)}^2\right)$
$=a^4-b^4$.

Hence, the statement is true.

Therefore, $1$ is the correct answer.