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?
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: