factor 25x^2y^2+95xy^2-150y^2

Question

ganeshie8 · Answer

start by pulling out the GCF

ganeshie8 · Answer

you have 3 terms there right ?
wats the common  thing in all 3 terms ?

anonymous · Answer

y^2

ganeshie8 · Answer

Yup !
factor that out first

ganeshie8 · Answer

$ 25x^2y^2+95xy^2-150y^2 $

$y^2( 25x^2+95x-150) $

ganeshie8 · Answer

also looks like we can take out 5 also

anonymous · Answer

y(y+?)(y-?) something like that right?

ganeshie8 · Answer

$ 25x^2y^2+95xy^2-150y^2 $

$y^2( 25x^2+95x-150) $

$5y^2( 5x^2+19x-30) $

anonymous · Answer

how did u get that?

ganeshie8 · Answer

25 = 5*5
95 = 5*19
150 = 5*30

ganeshie8 · Answer

ive just factored out the 5, like we factored the y^2 before

anonymous · Answer

it was wrong ;(

ganeshie8 · Answer

we're not done yet :o

anonymous · Answer

ooooh lol

ganeshie8 · Answer

:)

$ 25x^2y^2+95xy^2-150y^2 $

$y^2( 25x^2+95x-150) $

$5y^2( 5x^2+19x-30) $

ganeshie8 · Answer

fine so far right ?

anonymous · Answer

yes :)

anonymous · Answer

i really appreciate ur help btw. :)

ganeshie8 · Answer

now, think of two numbers such that :

sum = 19
product = 5(-30) =  -150

ganeshie8 · Answer

25 - 6 = 19
25(-6) = -150

so these are the magic numbers here

ganeshie8 · Answer

$ 25x^2y^2+95xy^2-150y^2 $

$y^2( 25x^2+95x-150) $

$5y^2( 5x^2+19x-30) $

$5y^2( 5x^2+25x - 6x -30) $

$5y^2( 5x(x+5) - 6(x+5)) $

$5y^2( (x+5)(5x-6)) $

$5y^2 (x+5)(5x-6) $

ganeshie8 · Answer

we're done. looks that was mouthful :o
see if it makes some sense :)

anonymous · Answer

it does ! thank u soooo much!

ganeshie8 · Answer

glad to hear ! np  you're wlc :)