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Expanding and factoringAlgebraHigh schoolabout 0:38

Factor x^2 - 9: animated lesson

A narrated, step-by-step expanding and factoring video lesson with captions. Final answer: (x - 3)(x + 3).

SpeedLanguage

Video with a synthetic English voice and captions. Pick another language for subtitles in that language, or open the interactive version.

Video narrated by a synthetic voice (Piper TTS, en_US-ljspeech-high voice (LJ Speech dataset, public domain)); the steps come from our maths engine and the answer was checked independently. Download MP4 (0.2 MB) · Captions (WebVTT)

Steps on screen

1. The problem
Worked example
$x^{2} - 9$
2. Step by step
1. $x^{2} - 9$
  Write the polynomial in standard form
2. Recognise a special pattern
3. $(x - 3)(x + 3)$
  Write the complete factorization
3. The answer
$(x - 3)(x + 3)$
x^2 - 9 = (x - 3)(x + 3)
4. Check
- Expanding (x - 3)(x + 3) gives back x^2 - 9.

Transcript

The problem. Here is the problem: x squared minus 9. Factor a polynomial over the rational numbers.

Step by step. Write the polynomial in standard form. Recognise a special pattern. The remaining factor is a difference of squares: a squared minus b squared equals (a minus b)(a plus b). Write the complete factorization.

The answer. So the answer is (x minus 3)(x plus 3). x squared minus 9 factors completely over the rationals as (x minus 3)(x plus 3).

Check. Expanding (x minus 3)(x plus 3) gives back x squared minus 9.

About expanding and factoring

Expand products of brackets and factor polynomials completely.

Factor x^2 - 9: Expanding and factoring Step-by-Step Lesson