How to Square a Polynomial

Save

Taking the square of a polynomial with n terms (a + b + c + ... n) is essentially a more complicated version of FOIL (First, Outside, Inside, Last) for multiplying binomials. It is a common mistake in algebra to write (a + b)^2 = a^2 + b^2; in fact, it is a^2 + 2ab + b^2. The inner term 2ab comes from using FOIL to expand the product of the two terms. Using a similar method for longer polynomials results in several inner terms.

  • Rewrite the square of the polynomial as the polynomial multiplied by itself. For example, rewrite (x^2 - 2x + 3)^2 as (x^2 - 2x + 3)(x^2 - 2x + 3).

  • Multiply the first term of the first polynomial by each term in the second polynomial, then add the products together. In the above example, multiply x^2 by x^2, -2x and 3 to get x^4 - 2x^3 + 3x^2.

  • Multiply the next term of the first polynomial by each term of the second polynomial. Add the products, then add the sum to the polynomial from step 2. In the example, you find -2x^3 + 4x^2 - 6x as the new terms.

  • Continue multiplying terms in the first polynomial by each term in the second polynomial until going through the entire polynomial. In the above example, the finished polynomial is x^4 - 2x^3 + 3x^2 - 2x^3 + 4x^2 - 6x + 3x^2 - 6x + 9.

  • Combine like terms to find the simplified version of the polynomial. Each of the terms, except for the highest-degree term (x^4 in the example) and the constant (9 in the example), appears exactly twice in the expanded polynomial. Simplifying the above polynomial yields the solution (x^2 - 2x + 3)^2 = x^4 - 4x^3 + 10x^2 - 12x + 9.

References

  • Photo Credit Jupiterimages/Photos.com/Getty Images
Promoted By Zergnet

Comments

You May Also Like

  • How to Find Roots of Polynomials

    A polynomial is a sum of terms containing variables with positive exponents. A quadratic is a polynomial with exponents going up to...

  • How to Find a Perfect Square Trinomial

    A trinomial is a polynomial, or algebraic expression with exactly three terms. A perfect square trinomial is one that has a squared...

  • How to Do Polynomial Operations

    Polynomial operations include multiplication, division, subtraction and addition. Learn how to do polynomial operations with help from a mathematician in this free...

  • What Does It Mean to Square a Monomial?

    Squaring a monomial means that you're multiplying that number by itself. Learn what it means to square a monomial with help from...

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!