factorise the following and also show how you did it?

Question

1)(p+q)^2-(a-b)^2+p+q-a+b=?
2)(x+2y)^2-1=?

Answer 1

1.(p+q)(p+q+1)[taking out p+q common between (p+q)^2 and p+q]-(a-b)(a-b-1)[taking out a-b common between (a-b)^2and -(a-b)]
=>(p+q)(p+q+1)+(a-b)(a-b-1)
2.[((x+2y)^2-1^2] now usngthe difference in squares
=(x+2y+1)(x+2y-1)

Answer 2

1>(p+q)^2 + (p+q) - [(a-b)^2 + (a-b)]
take (p+q) common from first two terms and (a-b) common from next 2.
(p+q)(p+q+1) -(a-b)(a-b+1)
I know this is not factorized form, but i cannot do any further.

2> (x+2y)^2 -1
=(x+2y+1)(x+2y-1)
{In general, a^2 - b^2 = (a+b)(a-b)}

Answer 3

1) put p+q=x
and a-b=y
x^2-y^2+x-y
=(x+y)(x-y)+(x-y)
=(x-y)(x+y+1)
=(p+q-a+b)(p+q+a-b+1)
2)(x+2y)^2-1
=(x+2y)^2-(1)^2
=(x+2y+1)(x+2y-1)