Confused need help factoring!!?

Question

x^4 - y^4 + 5x^2 - 5y^2

Answer 1

Mmmmmm...fun....factoring by grouping

Factor x^4 - y^4 = (x^2 - y^2) (x^2 + y^2)

Factor 5x^2 - 5y^2 = 5 ( x^2 - y^2)

so (x^2 - y^2) (x^2 + y^2) + 5 ( x^2 - y^2)

Now factor out the common factor of ( x^2 - y^2)

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

Now factor ( x^2 - y^2) so you get

SOLUTION :  (x + y) (x - y )  ( x^2 + y^2 + 5)

Good luck to you !!

Answer 2

x^4 - y^4 + 5x^2 - 5y^2

rearrange the problem to put x's together and y's together

x^4 + 5x^2 -y^4 -5y^2

factor out an x^2 and a -y^2

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

Answer 3

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

You can further factor (x^2-y^2) into (x+y)(x-y)

Your final equatio is (x+y)(x-y)(x^2+y^2)-5(x+y)(x-y)

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

Answer 4

= x^4 - y^4 + 5x^2 - 5y^2

= ([x^2 + y^2][x^2 - y^2]) + (5[x^2 - y^2])

= ([x^2 + y^2][x + y][x - y]) + (5[x + y][x - y])

= (x² + y² + 5)(x + y)(x - y)

Answer: (x² + y² + 5)([x + y][x - y])