Question

Divide using factorization method

Answer 1

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Answer 2

Given,

Divisor = 2(x - y)

Dividend = (3x - y)^2 - (x+y)^2

To find,

Quotient when dividend is divided by divisor.

Main solution :

Let's write it in form of p/q (i.e a form of a rational no. )

$\frac{{(3x - y)}^{2}- {(x +y)}^{2}}{2(x - y)}$

We can see that the numerator is in the form of a^2 - b^2

We know,

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

Using this identity :

$\frac{(3x - y + x + y)(3x - y - (x + y)}{2(x - y)}$

Simplyfying numerator:-

$\frac{4x(3x - y - x - y)}{2(x + y)}$

$\frac{4x(2x - 2y)}{2(x - y)}$

Taking 2 common in numerator.

$\frac{4x \times 2(x - y)}{2( x - y)}$

Cancelling numerator and denominator by 2 ( x - y ) as it is common to both

We get :

$\frac{4x}{1}$

$4x$

Answer :- The quotient is 4x