Factor 8+36x+54x^2+27x^3

$8 + 36 x + 54 x^{2} + 27 x^{3}$

Regroup terms.

$8 + 27 x^{3} + 36 x + 54 x^{2}$

Rewrite $8$ as $2^{3}$ .

$2^{3} + 27 x^{3} + 36 x + 54 x^{2}$

Rewrite $27 x^{3}$ as ${(3 x)}^{3}$ .

$2^{3} + {(3 x)}^{3} + 36 x + 54 x^{2}$

Since both terms are perfect cubes, factor using the sum of cubes formula, $a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ where $a = 2$ and $b = 3 x$ .

$(2 + 3 x) (2^{2} - 2 (3 x) + {(3 x)}^{2}) + 36 x + 54 x^{2}$

Simplify.

Raise $2$ to the power of $2$ .

$(2 + 3 x) (4 - 2 (3 x) + {(3 x)}^{2}) + 36 x + 54 x^{2}$

Multiply $3$ by $- 2$ .

$(2 + 3 x) (4 - 6 x + {(3 x)}^{2}) + 36 x + 54 x^{2}$

Apply the product rule to $3 x$ .

$(2 + 3 x) (4 - 6 x + 3^{2} x^{2}) + 36 x + 54 x^{2}$

Raise $3$ to the power of $2$ .

$(2 + 3 x) (4 - 6 x + 9 x^{2}) + 36 x + 54 x^{2}$

Factor $18 x$ out of $36 x + 54 x^{2}$ .

Factor $18 x$ out of $36 x$ .

$(2 + 3 x) (4 - 6 x + 9 x^{2}) + 18 x (2) + 54 x^{2}$

Factor $18 x$ out of $54 x^{2}$ .

$(2 + 3 x) (4 - 6 x + 9 x^{2}) + 18 x (2) + 18 x (3 x)$

Factor $18 x$ out of $18 x (2) + 18 x (3 x)$ .

$(2 + 3 x) (4 - 6 x + 9 x^{2}) + 18 x (2 + 3 x)$

Factor $2 + 3 x$ out of $(2 + 3 x) (4 - 6 x + 9 x^{2}) + 18 x (2 + 3 x)$ .

Factor $2 + 3 x$ out of $18 x (2 + 3 x)$ .

$(2 + 3 x) (4 - 6 x + 9 x^{2}) + (2 + 3 x) (18 x)$

Factor $2 + 3 x$ out of $(2 + 3 x) (4 - 6 x + 9 x^{2}) + (2 + 3 x) (18 x)$ .

$(2 + 3 x) (4 - 6 x + 9 x^{2} + 18 x)$

Add $- 6 x$ and $18 x$ .

$(2 + 3 x) (4 + 9 x^{2} + 12 x)$

Factor using the perfect square rule.

Rearrange terms.

$(2 + 3 x) (4 + 12 x + 9 x^{2})$

Rewrite $4$ as $2^{2}$ .

$(2 + 3 x) (2^{2} + 12 x + 9 x^{2})$

Rewrite $9 x^{2}$ as ${(3 x)}^{2}$ .

$(2 + 3 x) (2^{2} + 12 x + {(3 x)}^{2})$

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$12 x = 2 \cdot 2 \cdot (3 x)$

Rewrite the polynomial.

$(2 + 3 x) (2^{2} + 2 \cdot 2 \cdot (3 x) + {(3 x)}^{2})$

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = 2$ and $b = 3 x$ .

$(2 + 3 x) {(2 + 3 x)}^{2}$

Factor 8+36x+54x^2+27x^3

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