Rewriting by Structure

Aligned to A-SSE.A.2 — Common Core State Standards for Mathematics.

What this lesson teaches

Recognizing a pattern lets you rewrite an expression quickly. A difference of squares a^2 − b^2 always factors as (a + b)(a − b).

Example 1

Factor x^2 − 49. Since 49 = 7^2, this is a difference of squares: x^2 − 7^2 = (x + 7)(x − 7).

Example 2

Factor x⁴ − 16 as (x² − 4)(x² + 4), then again: (x−2)(x+2)(x²+4).

Example 3

x² + 49 is not a difference of squares and does not factor over the real numbers. Recognising what will not factor saves time.

Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.

Reconocer un patrón te permite reescribir una expresión rápidamente. Una diferencia de cuadrados a^2 − b^2 siempre se factoriza como (a + b)(a − b).

Ejemplo 1: Factoriza x^2 − 49. Como 49 = 7^2, esto es una diferencia de cuadrados: x^2 − 7^2 = (x + 7)(x − 7).

Ejemplo 2: Factoriza x⁴ − 16 como (x² − 4)(x² + 4), y otra vez: (x−2)(x+2)(x²+4).

Ejemplo 3: x² + 49 no es diferencia de cuadrados y no se factoriza en los reales. Reconocer lo que no se factoriza ahorra tiempo.

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