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Expanding and factoringAlgebraHigh schoolabout 1:08

Expand (x + y + 1)^2: animated lesson

A narrated, step-by-step expanding and factoring video lesson with captions. Final answer: x^2 + 2xy + y^2 + 2x + 2y + 1.

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+1)2{\left( x+ y+1\right)}^{2}
  2. 2. Step by step
    1. (x+y+1)2{\left( x+ y+1\right)}^{2}
      Read the expression
    2. Expand powers of sums
    3. x2+2xy+2x+y2+2y+1x^{2} + 2xy + 2x + y^{2} + 2y + 1
      Result after multiplying out
    4. x2+2xy+y2+2x+2y+1x^{2} + 2xy + y^{2} + 2x + 2y + 1
      Write the result in standard form
  3. 3. The answer
    x2+2xy+y2+2x+2y+1x^{2} + 2xy + y^{2} + 2x + 2y + 1

    (x + y + 1)^2 = x^2 + 2xy + y^2 + 2x + 2y + 1

  4. 4. Check
    • Spot check at x = 0.73, y = 1.14: original 8.2369, simplified 8.2369 ✓

Transcript

The problem. Here is the problem: (x plus y plus 1) squared. Expand (x plus y plus 1) squared 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 squared plus 2xy plus y squared plus 2x plus 2y plus 1. After expanding and combining like terms the expression is x squared plus 2xy plus y squared plus 2x plus 2y plus 1, a polynomial of degree 2 with 6 terms.

Check. Spot check at x equals 0.73, y equals 1.14: original 8.2369, simplified 8.2369, which checks out.

About expanding and factoring

Expand products of brackets and factor polynomials completely.

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Expand (x + y + 1)^2: Animated Step-by-Step Lesson