Algebra 1 Honors Lesson

Factoring Special Cases: Difference of Squares & Perfect Square Trinomials

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9-10BTC Style / Thinking Classrooms7-7 A1.PAFR.2.1 Transform linear, quadratic, exponential, and linear absolute value functions to equivalent forms to identify slope and yintercept for linear, vertex, and roots (if any) for quadratic and linear absolute value, and y-intercept for exponential. A1.PAFR.2.2 Solve quadratic equations by completing the square, factoring, and the quadratic formula, explaining the connection between the zeros of the function derived from the equation, its linear factors (if it factors), the x-intercepts of its graph (if they exist), and the solutions (if any) to the corresponding quadratic equation.90 min

Learning Objective

Students will factor quadratic expressions using difference of squares and perfect square trinomial patterns, connect factors to zeros of the related quadratic function, and solve quadratic equations using these special-case factoring strategies.

Lesson Overview

Students progress from recognizing perfect squares and differences of squares to factoring perfect square trinomials and applying special-case factoring to solve quadratic equations. Each task changes exactly one variable to build pattern recognition before algebraic fluency.

Materials

Vertical whiteboards or large chart paper
Dry-erase markers (multiple colors)
Erasers or whiteboard cloths
Printed consolidation note sheets (one per student)
Pencils

Scaffolded Task Progression

1Task 1

Which of the following are perfect squares? Sort them into two groups — Perfect Square or NOT a Perfect Square.

4, 12, 25, 36, 50, x^{2}, x^{3}, 9 x^{2}, 4 x^{4}, 7 x^{2}

2Task 2

Expand each product. Look for a pattern in your answers.
a)

(x + 5) (x - 5)

(x + 3) (x - 3)

(x + 9) (x - 9)

What do you notice? What always disappears?

3Task 3

Use the pattern you found to factor each expression. Check by expanding.
a)

x^{2} - 49

x^{2} - 100

x^{2} - 1

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