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Expanding and factoringAlgebraHigh schoolabout 1:00

Expand (a+b)^2: animated lesson

A narrated, step-by-step expanding and factoring video lesson with captions. Final answer: a^2 + 2ab + b^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 (0.4 MB) · Captions (WebVTT)

Steps on screen

1. The problem
Worked example
${\left( a+\mathrm{b}\right)}^{2}$
2. Step by step
1. ${\left( a+\mathrm{b}\right)}^{2}$
  Read the expression
2. Expand powers of sums
3. $a^{2} + 2ab + b^{2}$
  Result after multiplying out
4. $a^{2} + 2ab + b^{2}$
  Write the result in standard form
3. The answer
$a^{2} + 2ab + b^{2}$
(a+b)^2 = a^2 + 2ab + b^2
4. Check
- Spot check at a = 0.73, b = 1.14: original 3.4969, simplified 3.4969 ✓

Transcript

The problem. Here is the problem: (a plus b) squared. Expand (a plus b) 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 a squared plus 2ab plus b squared. After expanding and combining like terms the expression is a squared plus 2ab plus b squared, a polynomial of degree 2 with 3 terms.

Check. Spot check at a equals 0.73, b equals 1.14: original 3.4969, simplified 3.4969, which checks out.

About expanding and factoring

Expand products of brackets and factor polynomials completely.

Expand (a+b)^2: Expanding and factoring Step-by-Step Lesson