Factorization Of Algebraic Expressions — Maths STD 9 — Question
Gujarat BoardEnglish MediumSTD 9MathsFactorization Of Algebraic Expressions1 Mark
Question
Write the value of $48^3-30^3-18^3$.
✓
Answer
The given expression is
$48^3-30^3-18^3$
Let $\mathrm{a}=48, \mathrm{~b}=-30$ and $\mathrm{c}=-18$. Then the given expression becomes $48^3-30^3-18^3=\mathrm{a}^3+\mathrm{b}^3+\mathrm{c}^3$
Note that
$a+b+c=48+(-30)+(-18)$
$=48-30-18$
$=0$
Recall the formula
$a^3+b^3+c^3-3 a b c=(a+b+c)\left(a^2+b^2+c^2-a b-b c-c a\right)$
when $a+b+c=0$, this becomes
$a^3+b^3+c^3-3 a b c=0 \cdot\left(a^2+b^2+c^2-a b-b c-c a\right)$
$=0$
$a^3+b^3+c^3=3 a b c$
So, we have the new formula
$a^3+b^3+c^3=3 a b c \text {, when } a+b+c=0$
Using the above formula, the value of the given expression is
$a^3+b^3+c^3=3 a b c$
$48^3-30^3-18^3=3 \cdot(48) \cdot(-30) \cdot(-18)$
$48^3-30^3-18^3=77760$
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