FOIL Method - Examples

Examples

The FOIL method is most commonly used to multiply linear binomials. For example,

\begin{align} (x + 3)(x + 5) \,&=\, x\cdot x \,+\, x\cdot 5 \,+\, 3 \cdot x \,+\, 3 \cdot 5 \\ &=\, x^2 + 5x + 3x + 15 \\ &=\, x^2 + 8x + 15 \end{align}

If either binomial involves subtraction, the corresponding terms must be negated. For example,

\begin{align} (2x-3)(3x-4) &= (2x)(3x)+(2x)(-4)+(-3)(3x)+(-3)(-4) \\ &= 6x^2 - 8x - 9x + 12 \\ &= 6x^2 - 17x + 12 \end{align}

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