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Expanding and factoringAlgebraHigh schoolabout 0:53

Expand (2x + 3)(x^2 - 4x + 5): animated lesson

A narrated, step-by-step expanding and factoring video lesson with captions. Final answer: 2x^3 - 5x^2 - 2x + 15.

SpeedLanguage

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 (0.3 MB) · Captions (WebVTT)

Steps on screen

1. The problem
Worked example
$\left(2x+3\right) \left({x}^{2}-4x+5\right)$
2. Step by step
1. $\left(2x+3\right) \left({x}^{2}-4x+5\right)$
  Distribute every product and power
2. $2x^{3} - 5x^{2} - 2x + 15$
  Combine like terms and order by degree
3. Read off the key features
3. The answer
$2x^{3} - 5x^{2} - 2x + 15$
(2x + 3)(x^2 - 4x + 5) = 2x^3 - 5x^2 - 2x + 15
4. Check
- Spot check at x = 2: original and expanded form both give 7.

Transcript

The problem. Here is the problem: (2x plus 3)(x squared minus 4x plus 5). 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 3, leading coefficient 2, constant term 15.

The answer. So the answer is 2x cubed minus 5x squared minus 2x plus 15. In standard form the polynomial is 2x cubed minus 5x squared minus 2x plus 15 (degree 3, leading coefficient 2, constant term 15).

Check. Spot check at x equals 2: original and expanded form both give 7.

About expanding and factoring

Expand products of brackets and factor polynomials completely.

Expand (2x + 3)(x^2 - 4x + 5): Animated Step-by-Step Lesson