Special Products

Learn and apply special products using equations, examples, and interpretation.

Lesson 4 of 53 parts Practice Flashcards

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Square of a Sum

Objective: Explain and use square of a sum in an Algebra 1 problem.

(a+b)²=a²+2ab+b²; the middle term appears twice from cross-products. The cross-products total 2ab.

Worked examples

Try itExample 1.1: Expand (x+4)². What is the constant term?Show answer

16. The constant is the square of the constant term. The answer is 16.

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Objective: Explain and use square of a sum in an Algebra 1 problem.

(a+b)²=a²+2ab+b²; the middle term appears twice from cross-products. The cross-products total 2ab.

Worked examples

Try itExample 1.1: Expand (x+4)². What is the constant term?Show answer

16. The constant is the square of the constant term. The answer is 16.

Objective: Explain and use square of a difference in an Algebra 1 problem.

(a−b)²=a²−2ab+b²; the final square remains positive while the middle term is negative. Positive, because (−b)(−b)=b².

Worked examples

Try itExample 2.1: Expand (x+2)². What is the constant term?Show answer

4. The constant is the square of the constant term. The answer is 4.

Objective: Explain and use conjugate product in an Algebra 1 problem.

(a+b)(a−b)=a²−b² because the opposite cross terms cancel. The cross-products ab and −ab cancel.

Worked examples

Try itExample 3.1: Factor x²−9. What is the positive root?Show answer

3. The real roots of a difference of squares are opposite values. The answer is 3.

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