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Expansions (Including Substitution) — MATHEMATICS STD 9 — Question

ICSE BoardEnglish MediumSTD 9MATHEMATICSExpansions (Including Substitution)2 Marks
Question
Simplify using following identity
$(a \pm b)\left(a^2 \pm a b+b^2\right)=a^3 \pm b^3$
$ \left(3 x-\frac{5}{x}\right)\left(9 x^2+15+\frac{25}{x^2}\right)$
✓

Answer

$ \left(3 x-\frac{5}{x}\right)\left(9 x^2+15+\frac{25}{x^2}\right)$
$ =\left(3 x-\frac{5}{x}\right)\left[(3 x)^2+(3 x)\left(\frac{5}{x}\right)+\left(\frac{5}{x}\right)^2\right]$
$ =(3 x)^3-\left(\frac{5}{x}\right)^3$
$ =27 x^3-\frac{125}{x^3}$

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