Question

Complete each factoring formula. $$x^{2}+2 x y+y^{2}=$$

   Complete each factoring formula.
$$x^{2}+2 x y+y^{2}=$$

College Algebra

College Algebra

R. David Gustafson,… 11th Edition

Chapter 0, Problem 5

Instant Answer

Solved by Expert Sarah Brown

07/14/2020

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This is a perfect square trinomial, which is a special type of trinomial that can be factored into the square of a binomial. Show more…

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Complete each factoring formula. $$x^{2}+2 x y+y^{2}=$$

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Key Concepts

Square of a Binomial

The square of a binomial refers to a product of two identical binomials, which when expanded yields a perfect square trinomial. Understanding this formula is fundamental in algebra, as it allows one to quickly transform an expression like x² + 2xy + y² into its compact, factored form, (x + y)².

Perfect Square Trinomial

A perfect square trinomial is an algebraic expression in the form a² + 2ab + b² that can be rewritten as the square of a binomial, (a + b)². Recognizing this pattern is important because it simplifies the process of factoring and solving quadratic equations, as the structure directly leads to a simpler expression.

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