Question

Factorize

(3m-n)square - (m-2n) square

Answer 1

a^2 - b^2 = (a+b)(a-b)

(3m-n)^2 - (m-2n)^2= (3m-n+m-2n)(3m-n-m+2n)

Answer 2

The factorize form is $(3m-n)^2-(m-2n)^2=(4m-3n)(2m+n)$

Step-by-step explanation:

Given : Expression $(3m-n)^2-(m-2n)^2$

To find : Factorize the expression ?

Solution :

Expression $(3m-n)^2-(m-2n)^2$

Applying algebraic property,

$a^2-b^2=(a+b)(a-b)$

Here, $a=3m-n$ and $b=m-2n$

$(3m-n)^2-(m-2n)^2=(3m-n+(m-2n))(3m-n-(m-2n))$

$(3m-n)^2-(m-2n)^2=(3m-n+m-2n)(3m-n-m+2n)$

$(3m-n)^2-(m-2n)^2=(4m-3n)(2m+n)$

Therefore, the factorize form is $(3m-n)^2-(m-2n)^2=(4m-3n)(2m+n)$

#Learn more

Factorise :(a+b)³ - a - b

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