How to Factor a Perfect Cube

Save

A perfect cube is a number that can be written as a^3. When factoring a perfect cube, you would get a a a, where "a" is the base. Two common factoring procedures dealing with perfect cubes are factoring sums and differences of perfect cubes. To do this, you will need to factor the sum or difference into a binomial (two-term) and trinomial (three-term) expression. You can use the acronym "SOAP" to assist in factoring the sum or difference. SOAP refers to the signs of the factored expression from left to right, with the binomial first, and stands for "Same," "Opposite" and "Always Positive."

  • Rewrite the terms so that they are both written in the form (x)^3, giving you an equation that looks like

    a^3 + b^3 or a^3 - b^3. For example, given x^3 -- 27, rewrite this as x^3 -- 3^3.

  • Use SOAP to factor the expression into a binomial and trinomial. In SOAP, "same" refers to the fact that the sign between the two terms in the binomial portion of the factors will be positive if it is a sum and negative if it is a difference. "Opposite" refers to the fact that the sign between the first two terms of the trinomial portion of the factors will be the opposite of the sign of the unfactored expression. "Always positive" means that the last term in the trinomial will be always positive.

    If you had a sum a^3 + b^3, then this would become (a + b)(a^2 - ab + b^2), and if you had a difference a^3 - b^3, then this would be (a - b)(a^2 + ab + b^2). Using the example, you would get (x-3)(x^2 + x*3 + 3^2).

  • Clean up the expression. You may need to rewrite numerical terms with exponents without them and rewrite any coefficients, like the 3 in x 3, in the proper order. In the example, (x-3)(x^2 + x 3 + 3^2) would become (x-3)(x^2 + 3x + 9).

References

Promoted By Zergnet

Comments

You May Also Like

  • How to Factor Perfect Squares in Algebra

    A fundamental skill in algebra is factoring polynomials. The student who masters the special formula To Factor a Perfect Square, as well...

  • How to Factor Cubed Roots

    To simplify a cubed root, you have to factor it. Factoring a cube root is like factoring any other number. The difference...

  • How to Factor Cube Functions

    Cube functions take the form ax^3 + bx^2 + cx + d = 0. You can find the solution(s) using methods such...

  • How to Factor Perfect-Square Trinomials

    Writing an algebraic expression as a product of two or more factors can help you to solve equations more easily. Perfect square...

  • How to Factor Binomial Cubes

    Factoring cubic equations is significantly more challenging than factoring quadratics -- there are no guaranteed-to-work methods like guess-and-check and the box method,...

  • How to Cube Binomials

    Algebra presents many unique challenges that a student will not have faced in earlier math classes. One such challenge is how to...

  • Factoring Cubes

    Factoring cubes can be intimidating, and the first step involves making sure that all terms are written in terms of cubes. Discover...

  • Factoring Cube Functions

    When factoring cubes, remember that the pattern is usually the same for both the sums and differences of the cubes. Find out...

  • How to Factor Cubed Roots

    To factor cubed roots, break down each term into common factors, find the perfect cube of each, and solve the problem until...

Related Searches

Check It Out

Can You Take Advantage Of Student Loan Forgiveness?

M
Is DIY in your DNA? Become part of our maker community.
Submit Your Work!