FOIL (Multiplying Binomials)
To multiply two binomials, multiply every term in the first by every term in the second — FOIL names those four products so you don’t miss any.
This is a free explanation of FOIL (Multiplying Binomials) — a preview, not the full interactive lesson. The lesson, practice, quizzes, and AI Tutor are inside the app.
Since each binomial has two terms, multiplying them gives four products. FOIL stands for First, Outer, Inner, Last — the four pairs of terms you multiply: the First terms of each binomial, the Outer (outermost) terms, the Inner (innermost) terms, and the Last terms.
After FOIL you always combine the Outer and Inner results, because both are plain “x” terms — they are like terms. The First product (an x² term) and the Last product (a number) are unlike either of them, so they stay as-is.
The most common mistake is forgetting to combine the Outer and Inner results. FOIL produces four terms, but the answer is not complete until those two like terms are added together.
Worked example
Multiply: (x + 2)(x + 3)
- First: x × x = x². Outer: x × 3 = 3x. Inner: 2 × x = 2x. Last: 2 × 3 = 6.
- Write all four products together: x² + 3x + 2x + 6.
- Combine the Outer and Inner results — they are like terms (both x): 3x + 2x = 5x.
x² + 5x + 6
On the test: FOIL appears on the GED & HiSET both directly and as the reverse of factoring trinomials.
This concept also comes up in Quadratic Equations.
Inside the app, FOIL (Multiplying Binomials) comes with:
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- Glossary — Plain-English definitions of every key term in the lesson.
- Formula sheet — The GED® & HiSET® formula sheets, on screen while you practice.
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- Math-fact flashcards — Quick drills for addition, multiplication, perfect squares, and square roots.
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