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Expanding and factoringAlgebraHigh schoolabout 0:47

Factor x^2y - xy^2: animated lesson

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

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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
$x^{2}y - xy^{2}$
2. Step by step
1. $x^{2}y - xy^{2}$
  Write the polynomial in standard form
2. $x^{2}y - xy^{2} = xy\left(x - y\right)$
  Factor out the greatest common factor
3. Factor the homogeneous part
4. $xy(x - y)$
  Write the factorization
3. The answer
$xy(x - y)$
x^2y - xy^2 = xy(x - y)
4. Check
- Expanding xy(x - y) gives back x^2y - xy^2.

Transcript

The problem. Here is the problem: x to the power 2y minus xy squared. Factor a two-variable polynomial.

Step by step. Write the polynomial in standard form. Factor out the greatest common factor. Every term is divisible by xy. Factor the homogeneous part. The remaining factor is homogeneous of degree 1, so set y equals 1, factor the one-variable polynomial x minus 1, then restore y so every term has degree 1. Write the factorization.

The answer. So the answer is xy(x minus y). x to the power 2y minus xy squared equals xy(x minus y).

Check. Expanding xy(x minus y) gives back x to the power 2y minus xy squared.

About expanding and factoring

Expand products of brackets and factor polynomials completely.

Factor x^2y - xy^2: Expanding and factoring Lesson