# 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:

= x^{2} + y^{2} + 2xy - 1

= (x + y)^{2} - 1^{2}

= (x + y + 1)(x + y - 1)

can u pls help with 2nd and third exprn?

Go to main content# 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:

= x^{2} + y^{2} + 2xy - 1

= (x + y)^{2} - 1^{2}

= (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:

= y^{2} - x^{2} + 2y + 1

= (y + 1)^{2} - x^{2}

= (y + 1 + x)(y + 1 - x)

= (x + y + 1)(-x + y + 1)

3rd expression:

= x^{2} - y^{2} + 2x + 1

= (x + 1)^{2} - y^{2}

= (x + y + 1)(x - y + 1)

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

Video explanation: