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Simplify:$ \frac{1.2 \times 1.2 \times 1.2-0.2 \times 0.2 \times 0.2}{1.2 \times 1.2+1.2 \times 0.2+0.2 \times 0.2} $
Given:
\( \frac{1.2 \times 1.2 \times 1.2-0.2 \times 0.2 \times 0.2}{1.2 \times 1.2+1.2 \times 0.2+0.2 \times 0.2} \)
To do:
We have to simplify the given expression.
Solution:
We know that,
$a^3 + b^3 = (a + b) (a^2 - ab + b^2)$
$a^3 - b^3 = (a - b) (a^2 + ab + b^2)$
Therefore,
$\frac{1.2 \times 1.2 \times 1.2-0.2 \times 0.2 \times 0.2}{1.2 \times 1.2+1.2 \times 0.2+0.2 \times 0.2}$
Let $a=1.2$ and $b=0.2$
This implies,
$\frac{1.2 \times 1.2 \times 1.2-0.2 \times 0.2 \times 0.2}{1.2 \times 1.2+1.2 \times 0.2+0.2 \times 0.2}=\frac{a^{3}-b^{3}}{a^{2}+a b+b^{2}}$
$=\frac{(a-b)(a^{2}+a b+b^{2})}{a^{2}+a b+b^{2}}$
$=a-b$
$=1.2-0.2$
$=1$
Hence,$\frac{1.2 \times 1.2 \times 1.2-0.2 \times 0.2 \times 0.2}{1.2 \times 1.2+1.2 \times 0.2+0.2 \times 0.2}=1$.
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