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Expanding and factoringAlgebraHigh schoolabout 0:44

Factor x^2 - 14x + 49: animated lesson

A narrated, step-by-step expanding and factoring video lesson with captions. Final answer: (x - 7)^2.

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
$x^{2} - 14x + 49$
2. Step by step
1. $x^{2} - 14x + 49$
  Write the polynomial in standard form
2. Recognise a special pattern
3. $(x - 7)^{2}$
  Write the complete factorization
3. The answer
$(x - 7)^{2}$
x^2 - 14x + 49 = (x - 7)^2
4. Check
- Expanding (x - 7)^2 gives back x^2 - 14x + 49.

Transcript

The problem. Here is the problem: x squared minus 14x plus 49. Factor a polynomial over the rational numbers.

Step by step. Write the polynomial in standard form. Recognise a special pattern. The remaining factor is a perfect square trinomial: a squared plus or minus 2ab plus b squared equals (a plus or minus b) squared. Write the complete factorization.

The answer. So the answer is (x minus 7) squared. x squared minus 14x plus 49 factors completely over the rationals as (x minus 7) squared.

Check. Expanding (x minus 7) squared gives back x squared minus 14x plus 49.

About expanding and factoring

Expand products of brackets and factor polynomials completely.

Factor x^2 - 14x + 49: Animated Step-by-Step Lesson