Question

6xcube-30xsquare+60x-48 and 3xcube-12square+21x-18

Answer 1

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

I hope you are understand my solution