Question

need help with these two Factoring questions, Factoring fully:
1. (m+n)^2-m-n
and
2. (a^2-13a)^2-900

Answer 1

# 1

(m+n)^2-m-n

(m+n)^2-1(m+n)

Do you see what to do next?

Answer 2

oh ya i see so i take the (m+n) as a common value and then put the rest in a seperate value! thanks so much jim! do u think u could help me out with the second one as well?

Answer 3

exactly, you factor out the GCF m+n to go from

(m+n)^2-1(m+n)

to

(m+n)(m+n-1)

and you're done with #1

Answer 4

# 2

(a^2-13a)^2-900

is the same as

(a^2-13a)^2-(30)^2

since 30^2 = 900

Answer 5

now use the difference of squares factoring rule

Answer 6

tell me what you get

Answer 7

okay so i'm now using the 30^2 instead of the 900?

Answer 8

yes and you're using this rule

a^2 - b^2 = (a-b)(a+b)

Answer 9

well i should use different variables

x^2 - y^2 = (x-y)(x+y)

Answer 10

in this case, x = a^2-13a and y = 30

Answer 11

now tell me what you get when you factor using this rule

Answer 12

okay just trying it out now

Answer 13

i got part of the answer correct but the other part is not correct, the answer i got was (a-9) (a-4) (a-10) (a+3) but i should have gotten (a-10) (a-3) (a+2) (a-15) what am i doing wrong in this case?

Answer 14

when you factor (a^2-13a)^2-(30)^2 using the difference of squares rule, you should get

(a^2-13a-30)(a^2-13a+30)

Answer 15

then you factor a^2-13a-30 to get (a-15)(a+2)

notice how -15 plus 2 = -13 and -15 times 2 = -30

Answer 16

and you factor a^2-13a+30 to get (a-10)(a-3)

notice how -10 plus -3 = -13 and -10 times -3 = 30

Answer 17

so that's why (a^2-13a-30)(a^2-13a+30) factors completely into (a-15)(a+2)(a-10)(a-3)

Answer 18

ohh okay thanks a lot i got the answer now thank you for your help :)

Answer 19

you're welcome