Lesson 7: 8-7 Factoring Special Products
Duration of Days: 4
Lesson Objective
Factor binomials that are differences of squares.
Factor trinomials that are perfect squares.
How can you factor any polynomial of the form a^2-b^2?
Describe how the middle term of a perfect square trinomial of the form a^2-2ab+b^2 relates to the first and last terms?
difference of two squares
perfect square trinomial
A.SSE.2 Use the structure of an expression to identify ways to rewrite it.
SAT questions related to multiplying binomials: 4-3-5, 6-3-15, 4-4-28, 5-4-35, 8-3-5, 1-3-15; factoring: 5-3-4, 3-3-7
Factoring a polynomial can be done more quickly if the polynomial fits one of these special product patterns: difference of two squares: a^2 - b^2 = (a+b)(a-b); perfect square trinomials: a^2+2ab+b^2 = (a+b)(a+b) or a^2-2ab+b^2 = (a-b)(a-b). If the terms of the original polynomial have a greatest common factor, factor it out before applying any other factoring technique.
Computer graphics designers use the combination of art and mathematics skills to design images and videos. Factoring can help to determine the dimensions and shapes of the figures they design.
Students should be reminded to look closely at the coefficients of the second term of a perfect square trinomial. Its sign determins whether that factors are in the form (a-b) or (a+b).
As scaffolded questions for each example to build conceptual understanding for students at all levels.
Practice: Exercises 1 -19
Exercises 54-62
McGraw Hill resources