Factorization Of Algebraic Expressions — Maths STD 9 — Question
Gujarat BoardEnglish MediumSTD 9MathsFactorization Of Algebraic Expressions1 Mark
Question
Write the value of $30^3 + 20^3 - 50^3.$
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Answer
The given expression is $30^3+20^3-50^3$ Let $a=30, b=20$ and $c=-50$.
Then the given expression becomes $30^3+20^3-50^3=a^3+b^3+c^3$
Note that $a+b+c=30+20+(-50)=30+20-50=0$
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 $a^3+b^3+c^3=3 a b c$, when $a+b+c=0$
Using the above formula, the value of the given expression is $a ^3+ b ^3+ c ^3=3 abc 30^3+20^3-50^3$
$=3 \cdot(30) \cdot(20) \cdot(-50) 30^3+20^3-50^3=-90000$
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