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प्रश्न
Simplify.
(4a − 3)3 − (4a + 3)3
उत्तर
It is known that,
\[\left(a + b \right)^3 = a^3 + b^3 + 3 a^2 b + 3a b^2 ; \left(a - b \right)^3 = a^3 - b^3 - 3 a^2 b + 3a b^2\]
\[\ \left(4a - 3 \right)^3 - \left(4a + 3 \right)^3 \]
\[ = \left(4a \right)^3 - \left(3 \right)^3 - 3 \times \left(4a \right)^2 \times 3 + 3 \times 4a \times \left(3 \right)^2 - \left\{\left(4a \right)^3 + \left(3 \right)^3 + 3 \times \left( 4a \right)^2 \times 3 + 3 \times 4a \times \left(3 \right)^2 \right\}\]
\[= 64 a^3 - 27 - 144 a^2 + 108 - 64 a^3 - 27 - 144 a^2 - 108\]
\[= -288 a^2 - 54\]
संबंधित प्रश्न
Simplify.
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