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Expanding and factoringAlgebraHigh schoolabout 0:48

Factor 9a^2 - 16b^2: animated lesson

A narrated, step-by-step expanding and factoring video lesson with captions. Final answer: (3a - 4b)(3a + 4b).

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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 (0.3 MB) · Captions (WebVTT)

Steps on screen

1. The problem
Worked example
$9a^{2} - 16b^{2}$
2. Step by step
1. $9a^{2} - 16b^{2}$
  Write the polynomial in standard form
2. Factor the homogeneous part
3. $(3a - 4b)(3a + 4b)$
  Write the factorization
3. The answer
$(3a - 4b)(3a + 4b)$
9a^2 - 16b^2 = (3a - 4b)(3a + 4b)
4. Check
- Expanding (3a - 4b)(3a + 4b) gives back 9a^2 - 16b^2.

Transcript

The problem. Here is the problem: 9a squared minus 16b squared. Factor a two-variable polynomial.

Step by step. Write the polynomial in standard form. Factor the homogeneous part. The remaining factor is homogeneous of degree 2, so set b equals 1, factor the one-variable polynomial 9a squared minus 16, then restore b so every term has degree 2. Write the factorization.

The answer. So the answer is (3a minus 4b)(3a plus 4b). 9a squared minus 16b squared equals (3a minus 4b)(3a plus 4b).

Check. Expanding (3a minus 4b)(3a plus 4b) gives back 9a squared minus 16b squared.

About expanding and factoring

Expand products of brackets and factor polynomials completely.

Factor 9a^2 - 16b^2: Expanding and factoring Lesson