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Expanding and factoringAlgebraHigh schoolabout 1:13

Expand (x - y)^3: animated lesson

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

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 (0.4 MB) · Captions (WebVTT)

Steps on screen

  1. 1. The problem
    Worked example
    (x−y)3{\left( x- y\right)}^{3}
  2. 2. Step by step
    1. (x−y)3{\left( x- y\right)}^{3}
      Read the expression
    2. Expand powers of sums
    3. x3−3x2y+3xy2−y3x^{3} - 3x^{2}y + 3xy^{2} - y^{3}
      Result after multiplying out
    4. x3−3x2y+3xy2−y3x^{3} - 3x^{2}y + 3xy^{2} - y^{3}
      Write the result in standard form
  3. 3. The answer
    x3−3x2y+3xy2−y3x^{3} - 3x^{2}y + 3xy^{2} - y^{3}

    (x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3

  4. 4. Check
    • Spot check at x = 0.73, y = 1.14: original -0.068921, simplified -0.068921 ✓

Transcript

The problem. Here is the problem: (x minus y) cubed. Expand (x minus y) cubed and collect like terms.

Step by step. Read the expression. Expand powers of sums. Write (a plus b) to the power n as repeated multiplication and multiply out; e.g. (a plus b) squared equals a squared plus 2ab plus b squared. Result after multiplying out. Write the result in standard form. Terms are ordered by descending total degree.

The answer. So the answer is x cubed minus 3x to the power 2y plus 3xy squared minus y cubed. After expanding and combining like terms the expression is x cubed minus 3x to the power 2y plus 3xy squared minus y cubed, a polynomial of degree 3 with 4 terms.

Check. Spot check at x equals 0.73, y equals 1.14: original negative 0.068921, simplified negative 0.068921, which checks out.

About expanding and factoring

Expand products of brackets and factor polynomials completely.

More lessons like this

Expand (x - y)^3: Animated Step-by-Step Lesson (High school)