Question

x² - 2xy + y²– 22. Factorize it​

Answer 1

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x^2+2xy+y^2-a^2+2ab-b^2

On grouping the terms ,

x^2+2xy+y^2-(a^2–2ab+b^2)………….(1)

But we know

(A+B)^2=A^2+2AB+B^2

On converting the equation (1) to the above form, we get

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

Again this is of the form

A^2-B^2=(A+B)(A-B)

Where

A=x+y

B=a+b

So the above equation becomes,

(x+y+a+b)(x+y-(a+b))

That is

=(x+y+a+b)(x+y-a-b).

So the factors of the equation are

(x+y+a+b) and (x+y-a-b).