show that. x²+2xy+y² - a²+2ab- b²/(x+y-a+b) is equal (X+y+a-b)
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Answer:
(x+y+a+b) and (x+y-a-b).
Step-by-step explanation:
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).
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