Question

Find the product :$(a^2+b^2)(a^4+b^4)(a+b)(a-b)$.

• A. $a^2-b^2$
• B. $a^8-b^8$
• C. $a^5-b^5$
• D. $a^6-b^6$

Answer 1

Answer: (B)

Given, $(a^2+b^2)(a^4+b^4)(a+b)(a-b)$.

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

Then,

$(a^2+b^2)(a^4+b^4)(a+b)(a-b)$

$=(a^2+b^2)(a^4+b^4)(a^2-b^2)$

$=(a^2+b^2)(a^2-b^2)(a^4+b^4)$

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

$=(a^4-b^4)(a^4+b^4)$

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

$=(a^8-b^8)$.

Therefore, option $B$ is correct.