Again Factoring help ?

Hi,
Problem : p^2 +p - (a + 1)(a +2)

Now LOOK (a + 2) - (a + 1) = a+ 2 - a - 1 = 1

Hence, p^2 + {(a + 2) - (a + 1)}p - (a + 2)(a + 1)

= p^2 + (a + 2)p - (a + 1)p - (a + 2)(a + 1)

= p{p + a + 2} - (a + 1) {p + a + 2}

= (p + a +2)(p - a - 1) <==FACTORED

Hope i helped u :)

Dhonilover, check your wording again!!!

(p-a-1)(p+a+2)

Answer:

-(a - p + 1)(a + p + 2)

p² + p - (a + 1)(a + 2)
= p² + p - (a² + 3a + 2)
= p² + p - a² - 3a - 2
= p² - a² + p- 3a - 2
=p² - a² - 2a -1 + p-a- 1
=p² - (a² + 2a +1 )+(p-a- 1)
=p² - (a + 1)²+(p-a- 1)
=(p + a + 1)(p - a - 1)+(p-a- 1)
=(p - a - 1)(p + a + 1+1)
=(p - a - 1)(p + a + 2)

p^2 + p - (a + 1)(a + 2)
= p^2 + p - (a^2 + a + 2a + 2)
= p^2 + p - a^2 - 3a - 2
= p^2 + ap + 2p - ap - a^2 - 2a - p - a - 2
= (p^2 + ap + 2p) - (ap + a^2 + 2a) - (p + a + 2)
= p(p + a + 2) - a(p + a + 2) - 1(p + a + 2)
= (p + a + 2)(p - a - 1)

= p(p+p)-(a+1)(a+2)
= (p-a-1)(p+a+2)

(p+a+2)(p-a+1)