How do you factorise these algebraic expressions? Please show alll working and steps.?

Question

I need gelp with these algebraic expressions. Factorise them. Show all working and steps to get the answer.

a) 6ef + 2en - 12mf - 4mn
b) 6cp - 9pq - 2ac + 3aq
c) 3ah -ak -3bh + bk

Thanks a lot in advance.

Answer 1

a)
6ef + 2en - 12mf - 4mn
2e(3f + n) - 4m(3f + n)
(2e - 4m)(3f + n)

b)
6cp - 9pq - 2ac + 3aq
3p(2c - 3q) - a(2c - 3q)
(3p - a)(2c - 3q)

c)
3ah -ak -3bh + bk
a(3h - k) - b(3h - k)
(a - b)(3h - k)

To check, just use the foil method again

Answer 2

I'll get you started with the first step:
a)2e(3f+n) - 4m(3f+n)
b)3p(2c-3q) - a(2c-3q)
c)a(3h-k) - b(3h-k)

If you notice these are all the same question asked 3 slighly different ways.

Answer 3

observe: it particularly is factoring the variation of two suitable squares. 4y² - 9 = (2y + 3) (2y - 3) 16x² - 25 = (4x + 5) (4x - 5) 80 one - x²y² = (9 + xy) (9 - xy) a²b²c² - d² = (abc + d) (abc - d) (a + b)² - 9 = (a + b + 3) (a + b - 3)

Answer 4

6ef + 2en - 12mf - 4mn=
6ef-12mf+2en-4mn=
6f(e-2m) +2n(e-2m)=
(6f+2n)(e-2m)=
2(3f+n)(e-2m)

use the same procedure for the other 2 equations.

Answer 5

take common terms in each of these
a) 2e(3f+n)-4m(3f+n)
=> (3f+n)(2e-4m)
b) 2c(3p-a)-3q(3p-a)
=> (3p-a)(2c-3q)
c)
3h(a-b)-k(a-b)
=> (a-b)(3h-k)