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Expansions (Including Substitution) — MATHEMATICS STD 9 — Question

ICSE BoardEnglish MediumSTD 9MATHEMATICSExpansions (Including Substitution)2 Marks
Question
Simplify : $( x + 6 )( x + 4 )( x - 2 )$
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Answer

Using identity :
$(x + a)(x + b)(x + c)$
$= x^3+ (a + b + c)x^2+ (ab+bc+ ca)x +abc$
$(x + 6)(x + 4)(x - 2)$
$= x^3+ (6 + 4 - 2)x^2+ [6 \times 4 + 4 \times (-2) + (-2) \times 6]x + 6 \times 4 \times (-2)$
$= x^3+ 8x^2+ (24 - 8 - 12)x - 48$
$= x^3+ 8x^2+ 4x - 48$

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