Equivalent Forms of Expressions
Aligned to A-SSE.B.3 — Common Core State Standards for Mathematics.
What this lesson teaches
Rewriting an expression in a different but equal form can reveal a hidden property — factoring shows the values that make it zero, and factoring out a common factor shows shared structure.
Worked examples
Example 1
Factor x^2 − 5x + 6 to find where it equals zero. It factors as (x − 2)(x − 3), so the expression is 0 when x = 2 or x = 3.
Example 2
Complete the square on x² − 6x + 5: (x − 3)² − 4. The vertex (3, −4) is now readable without graphing.
Example 3
Each form answers one question. Factored gives the zeros, vertex gives the extremum, standard gives the y-intercept.
Practice questions
- Factor x^2 + 7x + 12 and state where it equals zero.
- Factor x^2 − 9 and state where it equals zero.
- Rewrite 2x^2 + 8x by factoring out the greatest common factor.
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Formas Equivalentes de Expresiones
Reescribir una expresión en una forma distinta pero igual puede revelar una propiedad oculta: factorizar muestra los valores que la hacen cero, y sacar un factor común muestra su estructura compartida.
Ejemplo 1: Factoriza x^2 − 5x + 6 para hallar dónde vale cero. Se factoriza como (x − 2)(x − 3), así que la expresión es 0 cuando x = 2 o x = 3.
Ejemplo 2: Completa el cuadrado en x² − 6x + 5: (x − 3)² − 4. El vértice (3, −4) ahora se lee sin graficar.
Ejemplo 3: Cada forma responde una pregunta. La factorizada da los ceros, la de vértice da el extremo, la estándar da la intersección con y.
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