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Expanding and factoringAlgebraHigh schoolabout 0:58

Expand (2x-1)^4: animated lesson

A narrated, step-by-step expanding and factoring video lesson with captions. Final answer: 16x^4 - 32x^3 + 24x^2 - 8x + 1.

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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
${\left(2x-1\right)}^{4}$
2. Step by step
1. ${\left(2x-1\right)}^{4}$
  Distribute every product and power
2. $16x^{4} - 32x^{3} + 24x^{2} - 8x + 1$
  Combine like terms and order by degree
3. Read off the key features
3. The answer
$16x^{4} - 32x^{3} + 24x^{2} - 8x + 1$
(2x-1)^4 = 16x^4 - 32x^3 + 24x^2 - 8x + 1
4. Check
- Spot check at x = 2: original and expanded form both give 81.

Transcript

The problem. Here is the problem: (2x minus 1) to the power 4. Expand and simplify the polynomial into standard form.

Step by step. Distribute every product and power. Multiply each term of one factor by each term of the other; expand powers by repeated multiplication. Combine like terms and order by degree. Read off the key features. degree 4, leading coefficient 16, constant term 1.

The answer. So the answer is 16x to the power 4 minus 32x cubed plus 24x squared minus 8x plus 1. In standard form the polynomial is 16x to the power 4 minus 32x cubed plus 24x squared minus 8x plus 1 (degree 4, leading coefficient 16, constant term 1).

Check. Spot check at x equals 2: original and expanded form both give 81.

About expanding and factoring

Expand products of brackets and factor polynomials completely.

Expand (2x-1)^4: Expanding and factoring Step-by-Step Lesson