Please help me factor 9x^2 - 25y^2 + 10y - 1?

Question

it's

9x^2 - 25y^2 + 10y - 1

i've got the answer,

(3x-1+5y) (3x+1-5y)

i would like to know the process...

thanks a lot!

Answer 1

think of it like this...

(9x² - 25y²) + 10y - 1

( ____ + ____ ) ( ____ - ____ )

the two front terms should multiply to give you the first term of 9x² - 25y².

that is (3x + 5y) and (3y - 5y). those go in the front slots...

((3x + 5y) + ____ ) ((3x - 5y) - ____ )

now the second terms in each have to multiply to give me -1

((3x + 5y) + 1) ((3x - 5y) - 1)

or just

(3x + 5y - 1)(3x + 1 - 5y)

which is the same thing as you have

yeah, luckily the 10y is taken care of when you foil it back out.