Question

add x square y cube + x y squared and 2x y square + xy

Answer 1

 One common factor.   a x + a y = a (x + y) 

2:    Sevearl grouped common factor.   a x + a y + b x + b y = a(x + y) + b(x + y) = (a + b ) (x + y)

3:    Difference of two squares (1).   x 2 - y 2= (x + y)(x - y) 

4:    Difference of two squares (2).   (x + y) 2- z 2 = (x + y + z)(x + y - z) 

5:    Sum of two cubes.   x 3 + y 3 = (x + y)(x 2- x y + y 2) 

6:    Difference of two cubes.   x 3 - y 3 = (x - y)(x 2 + x y + y 2) 

7:    Difference of fourth powers.   x 4 - y 4 = (x 2 - y 2)(x 2 + y 2) = (x + y)(x - y)(x 2 + y 2) 
8:     Perfet square   x 2 + 2xy + y 2 = (x + y) 2

9:     Perfet square   x 2 - 2xy + y 2 = (x - y) 2

10:     Perfect cube   x 3 + 3x 2y + 3xy 2 + y 3= (x + y) 3

11:     Perfect cube   x 3 - 3x 2y + 3xy 2 - y 3 = (x - y) 3