MCQ
The product $(a+b)(a-b)\left(a^2-a b+b^2\right)\left(a^2+a b+b^2\right)$ is equal to:
- A$a^6+b^6$
- ✓$a^6-b^6$
- C$a^3-b^3$
- D$a^3+b^3$
✓
Answer
Correct option: B.
$a^6-b^6$
$(a+b)(a-b)\left(a^2-a b+b^2\right)\left(a^2+a b+b^2\right)$
$=\left(a^2-b^2\right)\left(a^2+b^2-a b\right)\left(a^2+b^2-a b\right)$
$=\left(a^2-b^2\right)\left\{\left(a^2+b^2\right)^2-(a b)^2\right\}$
$=\left(a^2-b^2\right)\left\{a^4+b^4+2 a^2 b^2-a^2 b^2\right\}$
$=\left(a^2-b^2\right)\left\{a^4+b^4+a^2 b^2\right\}$
$=\left\{a^6+a^2 b^4+a^4 b^2-b^2 a^4-b^6-b^4 a^2\right\}$
$=a^6-b^6$
Hence, correct option is $(b)$.
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