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Expanding and factoringAlgebraHigh schoolabout 0:43

Factor 4x^2 - 12x + 9: animated lesson

A narrated, step-by-step expanding and factoring video lesson with captions. Final answer: (2x - 3)^2.

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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
$4x^{2} - 12x + 9$
2. Step by step
1. $4x^{2} - 12x + 9$
  Write the polynomial in standard form
2. Recognise a special pattern
3. $(2x - 3)^{2}$
  Write the complete factorization
3. The answer
$(2x - 3)^{2}$
4x^2 - 12x + 9 = (2x - 3)^2
4. Check
- Expanding (2x - 3)^2 gives back 4x^2 - 12x + 9.

Transcript

The problem. Here is the problem: 4x squared minus 12x plus 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 perfect square trinomial: a squared plus or minus 2ab plus b squared equals (a plus or minus b) squared. Write the complete factorization.

The answer. So the answer is (2x minus 3) squared. 4x squared minus 12x plus 9 factors completely over the rationals as (2x minus 3) squared.

Check. Expanding (2x minus 3) squared gives back 4x squared minus 12x plus 9.

About expanding and factoring

Expand products of brackets and factor polynomials completely.

Factor 4x^2 - 12x + 9: Animated Step-by-Step Lesson