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Fundamental Concepts (Including Fundamental Operations) — MATHS STD 7 — Question

ICSE BoardEnglish MediumSTD 7MATHSFundamental Concepts (Including Fundamental Operations)5 Marks
Question
Evaluate:
(i) $(a+b)(a-b)$
(ii) $\left(a^2+b^2\right)(a+b)(a-b)$; using the result of (i).
(iii) $\left(a^4+b^4\right)\left(a^2+b^2\right)(a+b)(a-b)$; using the result of (ii).
✓

Answer

$(i) (a + b)(a - b)$
$= a (a - b) + b(a - b)$
$= a^2 - ab + ab - b^2$
$= a^2 - b^2$
$(ii) (a^2 + b^2)(a + b)(a - b)$
$= (a^2 + b^2)(a^2 - b^2) ...{from(i)}$
$= a2 (a^2 - b^2) + b^2 (a^2 - b^2)$
$= a^4 - a^2b^2 + a^2b^2 - b^4$
$= a^8 - a^4b^4 + a^4b^4 - b^8$
$= a^4 - b^4$
$(iii) (a^4 + b^4)(a^2 + b^2)(a + b)(a - b)$
$= (a^4 + b^4) (a^4 - b^4) ....{from(ii)}$
$= a^4 (a^4 + b^4) + b^4 (a^4 + b^4)$
$= a^8 - a^4b^4 + a^4b^4 - b^8$
$= a^8 - b^8$

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