Question

100+4x^2-16y^2-40x

Answer 1

4(20 + .... )
4 *20 = 80
this will not give you 100

Answer 2

thanks!

Answer 3

4(25+x^2-4y^2-10x)?

Answer 4

k forget about the 4 on the outside.

25 + x^2
= (x-5)^2

follow so far?

Answer 5

wait, no....(x-5)^2 is x^2-10x+25

Answer 6

ur right, you'd end up with imaginary numbers if you evaluated 25+x^2

Answer 7

it would be (x-5i)(x+5i)

Answer 8

yeah... so how does the problem factor though?

Answer 9

wait!

Answer 10

look

Answer 11

(x-5)^2 =
x^2 -10x +25 that means all that is missing is the -4y^2 ! (x-5)^2 takes care of the -10x

So, you end up with

4((x-5)^2 -4y^2)

Do you see what happened? The -10x got factored by the (x-5)^2
or in other words, you can "package" the 25 -10x AND x^2 into (x-5)^2 so you're only left with -4y^2 at the end!

Answer 12

aha!

Answer 13

thanks! and now it's difference of squares right?

Answer 14

you could simplify more if you wanted to

Answer 15

4(x-5-2y)(x-5+2y)?

Answer 16

yup!

Answer 17

thank you!

Answer 18

np