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Multiplication Formula Table

Overview

Introducing commonly used multiplication formulas.

Formulas

$$\begin{align} (a+b)^2 &=a^2+2ab+b^2 \\ (a-b)^2 &= a^2-2ab+b^2 \end{align}$$

$$\begin{equation} (a+b)(a-b)=a^2-b^2 \end{equation}$$

$$\begin{align} (a+b)^3 &= a^3+3a^2b+3ab^2+b^3 \\ (a-b)^3 &= a^3-3a^2b+3ab^2-b^3 \end{align}$$

$$\begin{equation} (a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca \end{equation}$$

$$\begin{align} (a+b)(a^2-ab+b^2) &= a^3+b^3 \\ (a-b)(a^2+ab+b^2) &= a^3-b^3 \end{align}$$

Proof

(1), (2)

$$\begin{align*} (a \pm b)^{2} &= (a \pm b)(a \pm b) \\ &= a^{2} \pm ab \pm ba + b^{2} \\ &= a^{2} \pm 2ab + b^{2} \end{align*}$$

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