Question

Which of the following are the factors of $36x^2-49y^2$?

• A. (x-2)(x-5)= – 7x + 10
• B. (x+2) (x-2) = - 4
• C. $(6x-7y)$
• D. $(7x+6y)$

Answer 1

Answer: (A), (C)

The correct options are
A

(x-2)(x-5)= – 7x + 10

C

$(6x-7y)$

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

$36x^2-49y^2=(6x{)}^2-(7y{)}^2$....(i)

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

$a^2=(6x{)}^2\Rightarrow a=6x$

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

$\Rightarrow (6x{)}^2-(7y{)}^2=(6x+7y)(6x-7y)$

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