1Cademy - Multiplying $$(y - 7)(y + 4)$$ Using the FOIL Method

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The FOIL Method for Multiplying Binomials

Example

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

Multiply $(y - 7)(y + 4)$ 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: $y \cdot y = y^2$ .

Step 2 — Outer: Multiply the outermost terms: $y \cdot 4 = 4y$ .

Step 3 — Inner: Multiply the innermost terms: $(-7) \cdot y = -7y$ .

Step 4 — Last: Multiply the last terms: $(-7) \cdot 4 = -28$ .

Writing all four products in order gives:

$y^2 + 4y - 7y - 28$

Step 5 — Combine like terms: The Outer and Inner products $4y$ and $-7y$ are like terms with different signs: $4 + (-7) = -3$ :

$y^2 - 3y - 28$

The result is $y^2 - 3y - 28$ . 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, $(-7) \cdot y$ produces the negative term $-7y$ , and $(-7) \cdot 4$ produces the negative constant $-28$ .

Updated 2026-04-29

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