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Expanding and factoringAlgebraHigh schoolabout 0:48

Factor x^2 - 5xy + 6y^2: animated lesson

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

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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
$x^{2} - 5xy + 6y^{2}$
2. Step by step
1. $x^{2} - 5xy + 6y^{2}$
  Write the polynomial in standard form
2. Factor the homogeneous part
3. $(x - 3y)(x - 2y)$
  Write the factorization
3. The answer
$(x - 3y)(x - 2y)$
x^2 - 5xy + 6y^2 = (x - 3y)(x - 2y)
4. Check
- Expanding (x - 3y)(x - 2y) gives back x^2 - 5xy + 6y^2.

Transcript

The problem. Here is the problem: x squared minus 5xy plus 6y 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 y equals 1, factor the one-variable polynomial x squared minus 5x plus 6, then restore y so every term has degree 2. Write the factorization.

The answer. So the answer is (x minus 3y)(x minus 2y). x squared minus 5xy plus 6y squared equals (x minus 3y)(x minus 2y).

Check. Expanding (x minus 3y)(x minus 2y) gives back x squared minus 5xy plus 6y squared.

About expanding and factoring

Expand products of brackets and factor polynomials completely.

Factor x^2 - 5xy + 6y^2: Animated Step-by-Step Lesson