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Q.

Factories: ${4 a}^{2} - 4 ab + b^{2} - {9 c}^{2} + 12 cd + {4 d}^{2}$

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a

(2a−b−3c−2d)(2a+b+3c+2d)

b

(2a−b+3c+2d)(2a+b−3c−2d)

c

(2a−b+3c−2d)(2a−b−3c+2d)

d

(2a+b+3c−2d)(2a−b+3c−2d)

answer is C.

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Detailed Solution

Given that,

{4 a}^{2} - 4 ab + b^{2} - {9 c}^{2} + 12 cd + {4 d}^{2}

We can write this as,

{4 a}^{2} - 4 ab + b^{2} - {(9 c}^{2} - 12 cd - {4 d}^{2})

=

{(2 a - b)}^{2} - {(3 c - 2 d)}^{2}

=(2a−b+3c−2d)(2a−b−3c+2d)
Hence (3) is the correct option.

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Factories: 4a2-4ab+b2-9c2+12cd+4d2