Question

Factor the polynomial. 7x^2 + 68xy - 20y^2

Answer 1

Factoring this down, would leave you with two happy expressions in parantheses. (x+10y)(7x-2y).

(AKA Factor out an x and a y to be able to simplify even more.)

Answer 2

We notice that it must be a product of 2 different thingummies
so we have
(  x+/-  y)(  x+-/  y)
we need to determine the spaces ad signs
we know that the signs are different since the end result is negative
so fidn the first one
7
factor
7=1 times 7
so we have
(1x+/-    y)(7x+/-    y)
factor end
-20=-1 and 20 or -2 and 10 or -4 and 5
we want the middle term to be positive so the bigger term must be positive

try the ones closest first
(x-4y)(7x+5y)
multiply out the middles and outers
5xy-28xy is not 68xy
try -2 and 10
(x+10y)(7x-2y)
multily middles and outers
-2xy and 70xy=68xy
correct

answer is (x+10y)(7x-2y)