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प्रश्न
Factorize each of the following algebraic expression:
9a4 − 24a2b2 + 16b4 − 256
योग
उत्तर
\[9 a^4 - 24 a^2 b^2 + 16 b^4 - 256\]
\[ = (9 a^4 - 24 a^2 b^2 + 16 b^4 ) - 256\]
\[ = [(3 a^2 )^2 - 2 \times 3 a^2 \times 4 b^2 + (4 b^2 )^2 ] - {16}^2 \]
\[ = (3 a^2 - 4 b^2 )^2 - {16}^2 \]
\[ = [(3 a^2 - 4 b^2 ) - 16][(3 a^2 - 4 b^2 ) + 16]\]
\[ = (3 a^2 - 4 b^2 - 16)(3 a^2 - 4 b^2 + 16)\]
\[ = (9 a^4 - 24 a^2 b^2 + 16 b^4 ) - 256\]
\[ = [(3 a^2 )^2 - 2 \times 3 a^2 \times 4 b^2 + (4 b^2 )^2 ] - {16}^2 \]
\[ = (3 a^2 - 4 b^2 )^2 - {16}^2 \]
\[ = [(3 a^2 - 4 b^2 ) - 16][(3 a^2 - 4 b^2 ) + 16]\]
\[ = (3 a^2 - 4 b^2 - 16)(3 a^2 - 4 b^2 + 16)\]
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