1. factor the expression x^3 + 8y^3

2. factor x^9 - 27y^6

3. factor 4x^2-9

1.Well, since the first one is the sum of two cubes, you write it of the form:

(a + b)(a^2 - ab + b^2).

The cube root of x^3 is x because x*x*x = x^3.

The cube root of 8y^3 is found by taking the cube root of 8 and the cube root of y^3 and multiplying them together.

So, cube root of 8 is 2 and cube root of y^3 is y. 2y*2y*2y = 8y^3.

As per the above terms, we should find a^2, ab and b^2.

Allow a=x and b=2y

a^2 = x*x = x^2

b^2 = 2y*2y = 4y^2

ab = x*2y = 2xy

Now, we just use substitution:

(x + 2y)(x^2 - 2xy + 4y^2). and we are done.