Question

$25x^2-4$ can be factorised as:

• A. (5a + 2) (5a + 2)
• B. (5a - 2) (5a - 2)
• C. (5a + 2) (5a - 2)
• D. (5a + 12) (5a - 12)

Answer 1

The correct option is C (5a + 2) (5a - 2)

The expression $25x^2-4$ can be written as,

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

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

$a^2=(5x{)}^2\Rightarrow a=5x$

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

$\Rightarrow$ $25x^2-4$ ​​​​​​=$(5x+2)(5x-2)$

Therefore, the factors of $25x^2-4$ ​​​​​​ are​ $(5x+2)$ and $(5x-2)$.