Factoring Squares and Grouped Expressions

Algebra Foundation

Algebra 1

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Algebra 1 · Unit 8 · Topic 8.4

Factoring Squares and Grouped Expressions

Recognizing a² − b² = (a − b)(a + b) and perfect-square trinomials can simplify factoring.

Definition and explanation

Recognizing a² − b² = (a − b)(a + b) and perfect-square trinomials can simplify factoring. Factoring by grouping works when separate groups produce a common factor.

Worked example

Factor x² − 10x + 25 = (x − 5)² because the middle term is −2(5)x. For x³ + 2x² + 3x + 6, grouping gives x²(x + 2) + 3(x + 2) = (x + 2)(x² + 3).

Common mistake

A sum of squares does not follow the difference-of-squares pattern over the real numbers.

Key takeaway

Recognizing a² − b² = (a − b)(a + b) and perfect-square trinomials can simplify factoring.

Explain each step of the worked example, then check the units, signs, and conditions that apply.

Further reading

Topic coverage was checked against the openly available OpenStax Elementary Algebra 2e and Algebra and Trigonometry 2e textbooks. The explanations and examples on this site are independently written; textbook prose, exercises, and artwork are not reproduced.