+140 i need to factor
x^3-5x^2-xy^2+5y^2
i grouped them like this
{x^3-xy^2}{-5x^2+5y^2}
then
x(x^2-y^2)-5(x^2+y^2)
followed by
x(x+y)(x-y)-5(x^2+y^2)
I'm not too sure if i did it right and would apreciate the help as this is for my learning guide
+23252 x3 - 5x2 - xy2 + 5y2
When you grouped them you got:
x3 - xy2 - 5x2 + 5y2
Now, when you factor out the minus sign from the last two terms, you should get:
x3 - xy2 - (5x2 - 5y2) <--- Notice the minus sign in from of the 5y2 term (because the minus was factored out)
Continuing:
x(x2 - y2) - 5(x2 - y2)
(x2 - y2)(x - 5)
(x + y)(x - y)(x - 5)
+23252 x3 - 5x2 - xy2 + 5y2
When you grouped them you got:
x3 - xy2 - 5x2 + 5y2
Now, when you factor out the minus sign from the last two terms, you should get:
x3 - xy2 - (5x2 - 5y2) <--- Notice the minus sign in from of the 5y2 term (because the minus was factored out)
Continuing:
x(x2 - y2) - 5(x2 - y2)
(x2 - y2)(x - 5)
(x + y)(x - y)(x - 5)
Factor the following:
x^3-5 x^2-x y^2+5 y^2
Factor terms by grouping. x^3-5 x^2-x y^2+5 y^2 = (5 y^2-x y^2)+(x^3-5 x^2) = x^2 (x-5)-y^2 (x-5):
x^2 (x-5)-y^2 (x-5)
Factor x-5 from x^2 (x-5)-y^2 (x-5):
(x-5) (x^2-y^2)
Factor the difference of two squares. x^2-y^2 = (x-y) (x+y):
Answer: |(x-y) (x+y) (x - 5)
