Skip to content
MathSolver Pro
  • Open the math solver
  • Ask the AI tutor
  • Find an AP course
  • Create a quiz
  • Open the calculator
  • Graphing Calculator
  • Browse all calculators
  • Read math guides
↑ ↓Enter to open · Esc to close
Solve a problem
Simplifying expressionsAlgebraHigh schoolabout 1:14

Simplify (a+b)^2 - (a-b)^2: animated lesson

A narrated, step-by-step simplifying expressions video lesson with captions. Final answer: 4ab.

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+b)2−(a−b)2{\left( a+\mathrm{b}\right)}^{2}-{\left( a-\mathrm{b}\right)}^{2}
  2. 2. Steps, part 1
    1. (a+b)2−(a−b)2{\left( a+\mathrm{b}\right)}^{2}-{\left( a-\mathrm{b}\right)}^{2}
      Read the expression
    2. Expand powers of sums
    3. a2+2ab+b2−a2+2ab−b2a^{2} + 2ab + b^{2} - a^{2} + 2ab - b^{2}
      Result after multiplying out
    4. Combine like terms
  3. 3. Steps, part 2
    1. 4ab4ab
      Write the result in standard form
  4. 4. The answer
    4ab4ab

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

  5. 5. Check
    • Spot check at a = 0.73, b = 1.14: original 3.3288, simplified 3.3288 ✓

Transcript

The problem. Here is the problem: (a plus b) squared minus (a minus b) squared. Simplify the polynomial expression in a, b.

Steps, part 1. 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. Combine like terms. a squared: 1 minus 1 equals 0; ab: 2 plus 2 equals 4; b squared: 1 minus 1 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 4ab. After expanding and combining like terms the expression is 4ab, a polynomial of degree 2 with 1 term.

Check. Spot check at a equals 0.73, b equals 1.14: original 3.3288, simplified 3.3288, which checks out.

About simplifying expressions

Simplify algebraic and rational expressions by collecting like terms and cancelling common factors.

More lessons like this

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