1Cademy - Multiplying $$(3pq + 5)(6pq - 11)$$ Using the FOIL Method

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The FOIL Method for Multiplying Binomials

Example

Multiplying $(3pq + 5)(6pq - 11)$ Using the FOIL Method

Multiply $(3pq + 5)(6pq - 11)$ using the FOIL method. Since both binomials contain two-variable monomial terms ( $pq$ ), each step involves multiplying terms with multiple variables.

Step 1 — First: Multiply the first terms of each binomial: $3pq \cdot 6pq = 18p^2q^2$ (multiply the coefficients $3 \cdot 6 = 18$ and apply the Product Property for Exponents to each variable: $p \cdot p = p^2$ and $q \cdot q = q^2$ ).

Step 2 — Outer: Multiply the outermost terms: $3pq \cdot (-11) = -33pq$ .

Step 3 — Inner: Multiply the innermost terms: $5 \cdot 6pq = 30pq$ .

Step 4 — Last: Multiply the last terms of each binomial: $5 \cdot (-11) = -55$ .

Writing all four products in order gives: $18p^2q^2 - 33pq + 30pq - 55$

Step 5 — Combine like terms: The Outer and Inner products ( $-33pq$ and $30pq$ ) are like terms because both contain the same variable structure $pq$ . Combine their coefficients ( $-33 + 30 = -3$ ) to obtain the simplified trinomial: $18p^2q^2 - 3pq - 55$

Updated 2026-06-21

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