Factor completely.27x3+12527x^3+125

( 3 x + 5 ) ( 9 x 2 − 15 x + 25 ) \left(3x+5\right)\left(9x^2-15x+25\right) ( 3 x + 5 ) ( 9 x 2 − 15 x + 25 )

Factor completely. 27 x 3 + 125 27x^3+125

Here we need to factor this polynomial completely. 27 x cubed plus 125. And since we have an x cubed variable, let's check and see if this is a sum of cubes. So first, is 27 x cubed a cube term? Yes. 27 x cubed has the factors three x times three x times three x. And is one twenty five a perfect cube? Yes. Because it has the factors five times five times five. Sometimes we can rewrite this as three x cubed plus five cubed. And since our cube terms are being added, we can factor it as a, so 3x, same sign, so plus b, five times a squared, so three x squared, opposite sign, so minus a times b, three x times five, and then always positive. So plus B squared, five squared. Simplifying, we'll get three X plus five times three x squared is nine x squared, minus three times five is 15 x plus five squared is 25. And that is our polynomial now in factored form.

Factor completely. 27 x 3 + 125 27x^3+125

( 3 x + 5 ) ( 9 x 2 − 15 x + 25 ) \left(3x+5\right)\left(9x^2-15x+25\right) ( 3 x + 5 ) ( 9 x 2 − 15 x + 25 )

( 27 x + 5 ) ( x 2 + 25 ) \left(27x+5\right)\left(x^2+25\right) ( 27 x + 5 ) ( x 2 + 25 )

( 3 x + 5 ) ( x 2 + 5 ) \left(3x+5\right)\left(x^2+5\right) ( 3 x + 5 ) ( x 2 + 5 )

7. Factoring

Factoring Special Products

Beginning Algebra

7. Factoring

Factoring Special Products

Struggling with Beginning Algebra?

Join thousands of students who trust us to help them ace their exams!

Multiple Choice

Factor completely.
$27 x cubed plus 125$

$(3 x - 5) (9 x^{2} + 15 x + 25)$

$$\left$(3x+5$\right$)$\left$(9x^2-15x+25$\right$)$

$$\left$(27x+5$\right$)$\left$(x^2+25$\right$)$

$$\left$(3x+5$\right$)$\left$(x^2+5$\right$)$

Verified step by step guidance

Identify the expression you need to factor as a sum or difference of cubes. The general forms are $a^3 + b^3$ for sum of cubes and $a^3 - b^3$ for difference of cubes.

Rewrite each term in the expression as a perfect cube, if possible. For example, express terms like \$8$ as $2^3$ or $x^3$ as $(x)^3$.

Use the sum of cubes formula: $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$, or the difference of cubes formula: $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$, depending on the sign in the expression.

Substitute the values of $a$ and $b$ from your rewritten cubes into the appropriate formula to write the factored form.

Simplify the factors if possible by expanding or combining like terms, but do not multiply out the entire expression unless asked.

4:13m

Watch next

Master Difference of Squares with a bite sized video explanation from Patrick Ford