Question

Which of the following represents the factorisation of
$63x^2-175y^2?$

• A. $7(x+5y)(x-5y)$
• B. $7(3x+5y)(x-5y)$
• C. $7(x+5y)(3x-5y)$
• D. $7(3x+5y)(3x-5y)$

Answer 1

The correct option is D $7(3x+5y)(3x-5y)$

Given, the expression is
$63x^2-175y^2.$
The given expression can be factorized as,
$63x^2-175y^2$
$=(3\times 3\times 7\times x\times x)-(5\times 5\times 7\times y\times y)$
Taking 7 as a common factor, we get
$=7\left[\right(3\times 3\times x\times x)-(5\times 5\times y\times y)$
$=7\left[\right(3x{)}^2-\left(5y{)}^2\right]$
$\text{[Using identity:}{a}^2-b^2=(a+b)(a-b)]$
$=7\left[\right(3x+5y\left)\right(3x-5y\left)\right]$
So, the factorized form of the given expression
$63x^2-175y^2\text{is}7(3x+5y)(3x-5y).$