Squares of Binomials Chapter 5 Section 5.6

Objective Students will find squares of binomials and factor perfect square trinomials

Vocabulary Perfect square trinomial

Concept A square of a binomial looks like (a + b)2. This means the same as (a + b)(a + b). The following slide explains a rule on how to solve a problem like this.

(a + b)2 = a2 + 2ab + b2 (a – b)2 = a2 – 2ab + b2 Concept (a + b)2 = a2 + 2ab + b2 (a – b)2 = a2 – 2ab + b2

Concept The expression on the right side of these equations are called perfect square trinomials because each expression has three terms and is the square of the binomial.

Example (x + 3)2 (7u – 3)2

Example (4s – 5t)2 (3p2 – 2q2)2

Concept This pattern will also be useful for factoring. This means you will take a trinomial and determine whether it can be written as the square of binomials. a2 + 2ab + b2 = (a + b)2 a2 – 2ab + b2 = (a – b)2 To test whether a trinomial is a perfect square, ask yourself the following three questions.

Concept 1. Is the first term a square? 2. Is the last term a square? 3. Is the middle term, neglecting the sign, twice the sum of the product of the first term and last term?

Example Decide whether a perfect square, then factor 4x2 – 20x + 25 64u2 + 72uv + 81v2

Questions

Assignment Worksheet