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Expanding and factoringAlgebraHigh schoolabout 1:10

Expand (a + 2b)(a - 2b): animated lesson

A narrated, step-by-step expanding and factoring video lesson with captions. Final answer: a^2 - 4b^2.

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
    (a+2b)(a−2b)\left( a+2\mathrm{b}\right) \left( a-2\mathrm{b}\right)
  2. 2. Steps, part 1
    1. (a+2b)(a−2b)\left( a+2\mathrm{b}\right) \left( a-2\mathrm{b}\right)
      Read the expression
    2. Distribute (multiply out every product)
    3. a2−2ab+2ab−4b2a^{2} - 2ab + 2ab - 4b^{2}
      Result after multiplying out
    4. Combine like terms
  3. 3. Steps, part 2
    1. a2−4b2a^{2} - 4b^{2}
      Write the result in standard form
  4. 4. The answer
    a2−4b2a^{2} - 4b^{2}

    (a + 2b)(a - 2b) = a^2 - 4b^2

  5. 5. Check
    • Spot check at a = 0.73, b = 1.14: original -4.6655, simplified -4.6655 ✓

Transcript

The problem. Here is the problem: (a plus 2b)(a minus 2b). Expand (a plus 2b)(a minus 2b) and collect like terms.

Steps, part 1. Read the expression. Distribute (multiply out every product). Each term in one factor multiplies each term in the other: a(b plus c) equals ab plus ac. Result after multiplying out. Combine like terms. ab: negative 2 plus 2 equals 0. Like terms have identical variables and exponents, so only their coefficients are added.

Steps, part 2. Write the result in standard form. Terms are ordered by descending total degree.

The answer. So the answer is a squared minus 4b squared. After expanding and combining like terms the expression is a squared minus 4b squared, a polynomial of degree 2 with 2 terms.

Check. Spot check at a equals 0.73, b equals 1.14: original negative 4.6655, simplified negative 4.6655, which checks out.

About expanding and factoring

Expand products of brackets and factor polynomials completely.

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Expand (a + 2b)(a - 2b): Animated Step-by-Step Lesson