1Cademy - Multiplying $$(n^2 + 4)(n - 1)$$ Using the FOIL Method

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The FOIL Method for Multiplying Binomials

Example

Multiplying $(n^2 + 4)(n - 1)$ Using the FOIL Method

Multiply $(n^2 + 4)(n - 1)$ using the FOIL method — the first binomial contains a squared term ( $n^2$ ) rather than a first-degree term, so the product will be a cubic polynomial instead of the usual quadratic.

Step 1 — First: Multiply the first terms of each binomial: $n^2 \cdot n = n^3$ .

Step 2 — Outer: Multiply the outermost terms: $n^2 \cdot (-1) = -n^2$ .

Step 3 — Inner: Multiply the innermost terms: $4 \cdot n = 4n$ .

Step 4 — Last: Multiply the last terms of each binomial: $4 \cdot (-1) = -4$ .

Writing all four products in order gives:

$n^3 - n^2 + 4n - 4$

Step 5 — Combine like terms: The four terms are $n^3$ , $-n^2$ , $4n$ , and $-4$ . Each has a different power of $n$ , so there are no like terms to combine.

The result is $n^3 - n^2 + 4n - 4$ . When one of the binomials contains a higher-degree term such as $n^2$ , the First product yields a term of degree 3 rather than degree 2. Despite this, the FOIL procedure works exactly the same way — it still produces four products that must be checked for like terms. Here, all four terms have distinct degrees (3, 2, 1, and 0), so the result remains a four-term polynomial.

Updated 2026-04-21

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OpenStax Elementary Algebra

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