Maths identities (urgent)20pts

1) Factorize the following expressions:
p^2 - q^2 + 4p + 4q <--grouping terms
=(p+q)(p-q)+4(p+q) <---a^2-b^2=(a+b)(a-b)
=(p+q)(p-q+4)

2) Factorize the following expressions:
a^2 - b^2 + bc - ac <--Grouping terms
=(a+b)(a-b)+c(b-a) <--a^2-b^2=(a+b)(a-b)
=(a+b)(a-b)-c(a-b)
=(a-b)(a+b-c)

3) Factorize the following expressions:
75(m - 3n)^2 - 27(2m - 5n)^2
= 3[25(m-3n)^2-9(2m-5n)^2] <---Find common factor
=3[5^2(m-3n)^2-3^2(2m-5n)^2]
=3{[5(m-3n)]^2-[3(2m-5n)]^2}
=3(5m-15n)^2-(6m-15n)^2 <---a^2-b^2=(a+b)(a-b)
=3(5m-15n+6m-15n)(5m-15n-6m+15n)
=3(11m-30n)(-m)
=-3m(11m-30n)

4) Factorize the following expressions:
3u^2 - 12v^2 - 6u + 12v
=3(u^2-4v^2-2u+4v) <----Find common factor
=3[u^2-(2v)^2-2u+4v] <----a^2-b^2=(a+b)(a-b)
=3[(u+2v)(u-2v)-2(u+2v)]
=3(u+2v)(u-2v-2)

1. p^2 - q^2 + 4p + 4q
= (p + q)(p - q) + 4(p + q)
= (p + q)(p - q + 4)
2. a^2 - b^2 + bc - ac
= (a + b)(a - b) - c(a - b)
= (a - b)(a + b - c)
3. 75(m - 3n)^2 - 27(2m - 5n)^2
= 3[25(m - 3n)^2 - 9(2m - 5n)^2]
= 3{ [5(m - 3n)]^2 - [3(2m - 5n)]^2}
= 3{ (5m - 15n + 6m - 15n)(5m - 15n - 6m + 15n)}
= 3(11m - 30n)(-m)
= 3m(30n - 11m).
4. 3u^2 - 12v^2 - 6u + 12v
= 3[u^2 - (2v)^2] - 6(u - 2v)
= 3(u - 2v)(u + 2v) - 6(u - 2v)
= 3(u - 2v)(u + 2v - 2).

1) (p+q)(4+p-q)

2)(a+b)(a-b-c)

3)3m(30n-11m)

4)3u(u-2)+12v(1-v)