I need help with this, anyone , please?

1. (2x+y) * ((2x+y) - (2y-3x))

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

Bear in mind that the original function has several zeroes that are not indicated in the factors, so they are not identical functions.

2. A lot of math is pattern recognition, and a lot of homework is just fighting with things so you will remember them when you see them again.

8x^2 - 2y^2/9 = 2(4x^2 - (y^-9)^2) The pattern is x^2 - y^2 and the factors are (x + y) * (x - y).

2 * (2x + (y^-3)) * (2x - (y^-3))

Edited to correct the powers. Don't forget to check stuff like that. They can be sneaky sometimes. They are -3, not -9.

1) GCF is (2x+y).

(2x+y)^2 - (2x+y)(2y-3x)

= (2x + y)[(2x + y) - (2y - 3x)]

= (2x + y)(2x + y - 2y + 3x)

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

2) GCF is 2.

8x^2 - 2y^2/9

= 2(4x^2 - y^2/9) <--- difference of 2 squares

= 2[(2x)^2 - (y/3)^2]

= 2(2x + y/3)(2x - y/3)

(2x+y)^2 - (2x+y)(2y-3x)

factor out (2x + y)

(2x + y) [(2x + y) - (2y - 3x)]

within the parentheses, apply the negative to the second expression (2y - 3x)

(2x + y) [(2x + y) - 2y + 3x)]

combine like terms within the parentheses

(2x + 3x) AND (y - 2y)

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

(2x + y)(5x - y) <====