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Polynomials — MATHS STD 9 — Question

Rajasthan BoardEnglish MediumSTD 9MATHSPolynomials1 Mark
Question
The product $(a + b)(a - b)(a^2 - ab + b^2)(a^2 + ab + b^2)$ is equal to:
✓

Answer

$(a + b)(a - b)(a^2 - ab + b^2)(a^2 + ab + b^2)$
$= (a^2 - b^2)(a^2 + b^2 - ab)(a^2 + b^2 - ab)$
$= (a^2 - b^2) \Big\{(a^2 + b^2)^2 - (ab)^2\Big\}$
$= (a^2 - b^2) {a^4 + b^4 + 2a^2b^2 - a^2b^2}$
$= (a^2 - b^2) {a^4 + b^4 + a^2b^2}$
$= {a^6 + a^2b^4 + a^4b^2 - b^2a^4 - b^6 - b^4a^2}$
$= a^6 - b^6$

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