Which of the following is the factor of $16 (2 p − 3 q) 2 − 4 (2 p − 3 q)$ ?

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4 (2 p - 3 q) (8 p - 12 q - 1)

4 (2 p + 3 q) (8 p + 12 q - 1)

4 (2 p + 3 q) (8 p + 12 q + 1)

4 (2 p + 3 q) (8 p - 12 q - 1)

answer is A.

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Detailed Solution

Given expression is

16 2 p − 3 q 2 − 4 2 p − 3 q

.
Writing prime factors of each term,

⇒ 16 2 p − 3 q 2 = 2 × 2 × 2 × 2 × 2 p − 3 q × 2 p − 3 q ⇒ 4 2 p − 3 q = 2 × 2 × 2 p − 3 q

H C F 16 2 p − 3 q 2, 4 2 p − 3 q = 2 × 2 × 2 p − 3 q

Taking HCF common,

⇒ 16 2 p − 3 q 2 − 4 2 p − 3 q ⇒ 4 × 2 p − 3 q 4 × 2 p − 3 q − 1 ⇒ 4 2 p − 3 q 8 p − 12 q − 1

Hence, factors of

16 2 p − 3 q 2 − 4 2 p − 3 q = 4 2 p − 3 q 8 p − 12 q − 1

.
Therefore, option 1 is correct.

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