Question

Factor by grouping.
14ax-y+2ay-7x

Answer 1

which terms have common factors?

Answer 2

first and fourth and second and third

Answer 3

ok so what is the common factor between:

14ax & -7x

and

-y & 2ay

Answer 4

x, y

Answer 5

SO

14ax-7y = x(14a-7)

and

-y+2ay = y(-1+2a)


is there another common factor in the first one,
i.e. between 14a & -7 ?

Answer 6

yes, 7

Answer 7

we have

14ax-y+2ay-7x

= [14ax-7x]+[-y+2ay]
= x[14a-7]+y[-1+2a]
= 7x[2a-1]+y[-1+2a]
= . . .

what do we get if we switch around the terms in [-1+2a] around,

Answer 8

7x(2a1-)+y(2a-1)
?

Answer 9

i know you mean

7x(2a-1)+y(2a-1)

can you see another common factor now?

Answer 10

yes that is what i meant. no i do not see another common factor

Answer 11

is there anything the same between
7x(2a-1) & y(2a-1) ?

Answer 12

2a-1

Answer 13

yes, imagine (for a second) that (2a-1) = z

7xz + yz

how would you factorize this?

Answer 14

i really dont know

Answer 15

as you can see, z is the common factor, so bring it out the front:

z(7x + y)

now just put back z = (2a-1)

Answer 16

(2a-1)(7x+y)

Answer 17

that is correct!

Answer 18

thanks so much.

Answer 19

if you want to check your answer, you could foil it, and you should get the expression in the question statement

Answer 20

alright great thanks