# Find the H.C.F. from x^2 + y^2 + 2xy - 1, y^2 - x^2 + 2y + 1, x^2 - y^2 + 2x + 1

1st expression:
= x2 + y2 + 2xy - 1
= (x + y)2 - 12
= (x + y + 1)(x + y - 1)

can u pls help with 2nd and third exprn?

Sure. Here are the 2nd and 3rd expressions:

2nd expression:
= y2 - x2 + 2y + 1
= (y + 1)2 - x2
= (y + 1 + x)(y + 1 - x)
= (x + y + 1)(-x + y + 1)

3rd expression:
= x2 - y2 + 2x + 1
= (x + 1)2 - y2
= (x + y + 1)(x - y + 1)

From above, the highest common factor (HCF) is (x + y + 1)

Video explanation:
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