factor the polynomial 8a cubed - 27?

8a^3 - 27 is the difference of two cubes [2a]^3 - [3]^3

Use the following formula:

A^3 - B^3 = (A - B)(A^2 + AB + B^2)

You can do it. Go for it.

element: 8 + y^3 8 + y^3 = 2^3 + y^3 we are waiting to element the above expression by means of utilizing the sum of a cube formula: a^3 + b^3 = (a + b)(a^2 - ab + b^2) 8 = 2 * 2 * 2 (for this reason 2 is a cube of 8) y = y * y * y (for this reason y is a cube of y^3) for this reason the respond is: (2 + y)(4 - 2y + y^2) or (y +2)(y^2 - 2y + 4)

a^3 - b^3 ≡ (a - b)(a^2 + ab + b^2)

8a^3 - 27
= (2a)^3 - 3^3
= (2a - 3)[(2a)^2 + (2a)(3) + 3^2]
= (2a - 3)(4a^2 + 6a + 9)

The first reply gave you a formula for the difference of two cubes.

A^3 - B^3 = (A - B)(A^2 + AB + B^2)

I will use that formula.

We need to have the SAME POWER.

So, 27 can be written as 3^3.

Also, 8a^3 can be written as 2^3(a^3) becoming 2a.

Do you see that we now have the same power or exponent of 3?

In the formula A = 2a and B = 3.

We now plug and chug.

A^3 - B^3 = (A - B)(A^2 + AB + B^2)

(2^3a^3 - 3^3) = (2a - 3)(4a^2 + 6a + 9)

The final answer is (2a - 3)(4a^2 + 6a + 9).

NOTE: If you multiply (2a - 3) by (4a^2 + 6a + 9), you'll end up with the original difference of cubes given. This is how you can check to see if the math work is correct. Why not try it?

8a³ - 27 is the difference between two cubes. One factor is (2a - 3).

Do the long division and get

8a³ - 27 = (2a - 3)(4a² + 6a + 9)

The quadratic factor does not have real roots.

Differences of cubes =
(a³ - b³) = (a - b)(a² + ab + b²)

(8a³ - 27) = (2³a³ - 3³)

(2³a³ - 3³) = (2a - 3)(4a² + 6a + 9) ---> Answer

This is the Difference of Cubes:
x³ - y³ = (x - y)(x² + xy + y²)

8a³ - 2y = (2a)³ - 3³
= (2a - 3)((2a)² + 2a3 + 3²)
= (2a - 3)(4a² + 6a + 9)