Mathematics

Binomial square formulas - formula in LaTeX

The square of a sum and of a difference in one line: read the upper signs together and the lower signs together. The plus-minus sign is \pm. If the same formula needs the flipped one, use \mp.

$$
(a\pm b)^2 = a^2 \pm 2ab + b^2
$$

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What the symbols mean

$a, b$

any numbers or expressions

A math formula - one of the most frequently typed in assignments, lecture notes and calculus or algebra homework.

Worked example

The square of a difference lets you work out 99² in your head. The multiplication dot is \cdot; a plain asterisk * stays an asterisk in LaTeX.

Other ways to write it

• The square of a sum on its own, when the text needs just one sign.

  $$(a+b)^2 = a^2 + 2ab + b^2$$

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

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• Difference of squares, often needed to simplify fractions.

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

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

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• Cube of a sum and of a difference in one line.

  $$(a\pm b)^3 = a^3 \pm 3a^2b + 3ab^2 \pm b^3$$

  (a\pm b)^3 = a^3 \pm 3a^2b + 3ab^2 \pm b^3

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• Sum and difference of cubes: this is where \mp is needed, since the sign in the second bracket is flipped.

  $$a^3 \pm b^3 = (a\pm b)(a^2 \mp ab + b^2)$$

  a^3 \pm b^3 = (a\pm b)(a^2 \mp ab + b^2)

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LaTeX commands in this formula

\pm

plus-minus sign

x^{2}

superscript (power); wrap several characters in braces

How to use this formula in LaTeX?

1. Copy the code with the button above - $$…$$ is centered display math.
2. Paste it into the CamteX editor, Overleaf or any LaTeX document.
3. Inside a sentence, use single $…$ instead of double.
4. The formula works without extra packages.

Related formulas - Mathematics

• Quadratic formula
• Product rule
• Definite integral
• 2×2 matrix
• System of equations