TOPICS
Search

Perfect Square Trinomial

A perfect square trinomial is a trinomial obtained by squaring a binomial. The two forms are a^2+2ab+b^2=(a+b)^2 and a^2-2ab+b^2=(a-b)^2. Thus its first and last terms are perfect squares, and its middle term is twice the product of their square roots, with either sign. For example,

x^2-10x+25=(x-5)^2.

is a perfect square trinomial.

Recognizing a perfect square trinomial is useful in polynomial factorization and in completing the square.

See also

Binomial, Completing the Square, Perfect Square, Polynomial Factorization, Trinomial

Explore with Wolfram|Alpha

References

Gelfand, I. M. and Shen, A. Algebra. Boston, MA: Birkhäuser, 1993.

Cite this as:

Weisstein, Eric W. "Perfect Square Trinomial." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PerfectSquareTrinomial.html

Subject classifications