Question

On factorising $25-49x^2$, we get

• A. (5x+7)(5x+2)
• B. (7x+5)(5x+3)
• C. (7x+5)²
• D. (3x+7)²

Answer 1

The correct option is C

(7x+5)²

The expression $25-49x^2$ can be written as

$5^2-(7x{)}^2$.....(i)

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

$a^2=5^2\Rightarrow a=5$

$b^2=(7x{)}^2\Rightarrow b=7x$

$\Rightarrow 5^2-(7x{)}^2=(5+7x\left)\right(5-7x)$

Therefore, the factors of $25-49x^2$ are $(5+7x)$ and $(5-7x)$.

i.e., $25-49x^2=5^2-(7x{)}^2=(5+7x\left)\right(5-7x)$