Factorize each of the following algebraic expression-9 a4-24 a2 b2-16 b4-256

#160; #160; #160; #160;9a4 24a2b2+16b4 256=(9a4 24a2b2+16b4) 256=[(3a2)2 2 #215;3a2 #215;4b2+(4b2)2] 162=(3a2 4b2)2 162=[(3a2 4b2) 16][(3a2 4b2)+16 ...

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Byju's Answer

Standard VIII

Mathematics

Factorisation by Common Factors

Factorize eac...

Question

Factorize each of the following algebraic expression:
9a⁴ − 24a²b² + 16b⁴ − 256

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Solution

$9 a^{4} - 24 a^{2} b^{2} + 16 b^{4} - 256 = (9 a^{4} - 24 a^{2} b^{2} + 16 b^{4}) - 256 = [(3 a^{2})^{2} - 2 \times 3 a^{2} \times 4 b^{2} + (4 b^{2})^{2}] - 16^{2} = (3 a^{2} - 4 b^{2})^{2} - 16^{2} = [(3 a^{2} - 4 b^{2}) - 16] [(3 a^{2} - 4 b^{2}) + 16] = (3 a^{2} - 4 b^{2} - 16) (3 a^{2} - 4 b^{2} + 16)$

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Factorize each of the following algebraic expression: 9a4 − 24a2b2 + 16b4 − 256

9a4-24a2b2+16b4-256=(9a4-24a2b2+16b4)-256=[(3a2)2-2×3a2×4b2+(4b2)2]-162=(3a2-4b2)2-162=[(3a2-4b2)-16][(3a2-4b2)+16]=(3a2-4b2-16)(3a2-4b2+16)

Factorize each of the following algebraic expression:
9a⁴ − 24a²b² + 16b⁴ − 256