factoring by grouping?help!?

=a(a-b)+a-b=(a-b)(a-1)
Good Luck.

(a+1)(a-b)

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

1)
a^2 - ab + a - b
= (a^2 - ab) + (a - b)
= a(a - b) + 1(a - b)
= (a - b)(a + 1)

2)
y^2 - x^2 - 2x - 1
= y^2 - (x^2 + 2x + 1)
= y^2 - (x^2 + x + x + 1)
= y^2 - [(x^2 + x) + (x + 1)]
= y^2 - [x(x + 1) + 1(x + 1)]
= y^2 - (x + 1)(x + 1)
= y^2 - (x + 1)^2
= [y^2 + (x + 1)][y^2 - (x + 1)]
= (y^2 + x + 1)(y^2 - x - 1)

a^2-ab+a-b=
a(a-b) + (a-b) = <<< by grouping we turn 4 terms into 2 terms with a binomial factor in common

(a+b)(a+1) <<< write the common factor first, then put together the other factor by dividing both terms from the previous step by (a-b)

y^2-x^2-2x-1=
y^2 - (x^2+2x+1) = <<< the last three terms form a TCP
y^2 - (x+1)^2 = <<<<<< difference of squares, roots are "y" and "(x+1)"
[y+(x+1)][y-(x+1)]
(y+x+1)(y-x-1)