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:
- ✓$a^6-b^6$
- B$a^3-b^3$
- C$a^6+b^6$
- D$a^3+b^3$
✓
Answer
Correct option: A.
$a^6-b^6$
$(a+b)(a-b)\left(a^2-a b+b^2\right)\left(a^2+a b+b^2\right)$
$\Rightarrow\left\{(a+b)\left(a^2+b^2-a b\right)\right\}\left\{(a-b)\left(a^2+b^2+a b\right)\right\}$
$\Rightarrow\left(a^3+b^3\right)\left(a^3-b^3\right)$
$\Rightarrow\left(a^6-b^6\right)$
$\Rightarrow\left\{(a+b)\left(a^2+b^2-a b\right)\right\}\left\{(a-b)\left(a^2+b^2+a b\right)\right\}$
$\Rightarrow\left(a^3+b^3\right)\left(a^3-b^3\right)$
$\Rightarrow\left(a^6-b^6\right)$
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