Question

Factors of $49p^2-36$ are:

• A. (7p - 6) (7p + 6)
• B. (7p - 6) (7p - 6)
• C. (7p + 6) (7p + 6)
• D. (6p - 7) (7p - 6)

Answer 1

Answer: (A), (B)

The correct options are
A

(7p - 6) (7p + 6)

B

(7p - 6) (7p - 6)

The expression $49p^2-36$ can be written as

$(7p{)}^2-6^2$....(i)

Comparing (i) with the identity $a^2-b^2=(a+b)(a-b)$, we get

$a^2=(7p{)}^2\Rightarrow a=7p$

$b^2=6^2\Rightarrow b=6$

$\Rightarrow 49p^2-36$=$(7p{)}^2-(6{)}^2$=$(7p-6)(7p+6)$

Therefore, the factors of $49p^2-36$ are $(7p+6)$ and $(7p-6)$.

This cannot be factorised into any further factors.