Example

Multiplying (y7)(y+4)(y - 7)(y + 4) Using the FOIL Method

Multiply (y7)(y+4)(y - 7)(y + 4) using the FOIL method — the first binomial involves a subtraction, which introduces negative terms among the four FOIL products.

Step 1 — First: Multiply the first terms: yy=y2y \cdot y = y^2. Step 2 — Outer: Multiply the outermost terms: y4=4yy \cdot 4 = 4y. Step 3 — Inner: Multiply the innermost terms: (7)y=7y(-7) \cdot y = -7y. Step 4 — Last: Multiply the last terms: (7)4=28(-7) \cdot 4 = -28.

Writing all four products in order gives: y2+4y7y28y^2 + 4y - 7y - 28.

Step 5 — Combine like terms: The Outer and Inner products 4y4y and 7y-7y are like terms with different signs: 4y+(7y)=3y4y + (-7y) = -3y. The simplified result is y23y28y^2 - 3y - 28.

When one binomial contains a subtraction, the Inner and Last products involve multiplying by a negative number, so careful attention to sign rules is essential. Here, (7)y(-7) \cdot y produces the negative term 7y-7y, and (7)4(-7) \cdot 4 produces the negative constant 28-28.

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Updated 2026-05-13

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