Question

how do you factor this

8x^3+27

Answer 1

That is (2x)^3 + 3^3

in general
a^3 + b^3 = a^3 + 3a^2b + 3ab^2 + b^3
so
(2x)^3 + 3(2x)^2(3) + 3 (2x)(3)^2 + 27
which is
8x^3 + 36x^2 + 18x + 27

Answer 2

I was thinking of binomial expansion. This is not.

a^3+b^3 = (a+b)(a^2-ab+b^2)

Answer 3

so

(2x+3)(4x^2-6x+9)

Answer 4

thanks!

Answer 5

[AI-generated answer — Explain Bot]

To factor the expression 8x^3 + 27, we can use the sum of cubes identity. The sum of cubes identity is given by:

a^3 + b^3 = (a + b)(a^2 - ab + b^2)

In this case, a = 2x and b = 3, and we can rewrite the expression as:

(2x)^3 + 3^3

Now we can substitute a = 2x and b = 3 into the sum of cubes formula:

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

Simplifying further, we have:

(2x + 3)(4x^2 - 6x + 9)

Thus, the factored form of the expression 8x^3 + 27 is (2x + 3)(4x^2 - 6x + 9).