How do you factor  27x^3 + 54 x^2 + 36x +8 by grouping?

Jun 19, 2016

Note that the first and last terms are perfect cubes and find:

$27 {x}^{3} + 54 {x}^{2} + 36 x + 8 = {\left(3 x + 2\right)}^{3}$

Explanation:

Notice that the ratio between the first and second coefficients is not the same as that between the third and fourth.

That is: $\frac{27}{54} \ne \frac{36}{8}$

So this does not factor by grouping.

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Note that the first and last terms are both perfect cubes:

$27 {x}^{3} = {\left(3 x\right)}^{3}$

$8 = {2}^{3}$

So we might try ${\left(3 x + 2\right)}^{3}$:

${\left(3 x + 2\right)}^{3} = 27 {x}^{3} + 54 {x}^{2} + 36 x + 8$

Yes - that's our factoring.