Question

Factor 8k3 + 27 by using an identity.
how to do it?

Answer 1

Answer:

The given expression is factored into $(2k+3)(4k^2-6k+9)$

Step-by-step explanation:

Given:

The expression to factor is given as:

$8k^3+27$

We observe that 8 = $2\times 2\times 2=2^3$

Also, $27 = 3\times 3\times 3=3^3$

So, the above expression can be rewritten as:

$(2k)^3+3^3$

The above expression is of the form $a^3+b^3$.

We know that the above identity is factored as:

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

Here, $a=2k\ and\ b=3$

Therefore, the given expression can be factored using the above identity and is factored as:

$(2k)^3+3^3=(2k+3)((2k)^2-(2k)(3)+3^2)\\\\(2k)^3+3^3=(2k+3)(4k^2-6k+9)$

Hence, the given expression is factored into $(2k+3)(4k^2-6k+9)$