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Stage 2 · Algebra Part 1

Multiplying Polynomials

Multiplication builds on two rules: multiply the coefficients and add the exponents. Once you have that, distributing to every term is all it takes.

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📖 Learn the Skill Lesson + examples ✏️ Foundations Practice Practice questions 🎯 GED Level Practice GED level questions

📖 The Key Rule — Exponents

When you multiply two terms with the same base, you add the exponents. This is the foundation of everything on this page.

Same Base → Add Exponents
x² · x³ = x^(2+3) = x⁵
Worked Examples — Exponent Rule
x · x = x^(1+1) = x²
x² · x³ = x^(2+3) = x⁵
x⁴ · x = x^(4+1) = x⁵

Multiplying Monomials

Multiply the coefficients separately, then add the exponents. Keep them in two separate steps.

Worked Example — Monomial × Monomial

Multiply: −3x · 2x²

−3x · 2x²
→ Step 1: Multiply coefficients — −3 × 2 = −6
→ Step 2: Add exponents — x¹ × x² = x^(1+2) = x³
= −6x³
Worked Example — Negative × Negative

Multiply: (−4x³) · (−3x²)

(−4x³) · (−3x²)
→ Negative × negative = positive
→ Coefficients: −4 × −3 = 12
→ Exponents: x³ × x² = x⁵
= 12x⁵

Monomial × Polynomial

Distribute the monomial to every term in the polynomial. Every term gets multiplied — no exceptions.

Worked Example — Monomial × Binomial

Multiply: −3x(2x − 1)

−3x(2x − 1)
→ Distribute −3x to every term
→ −3x · 2x = −6x² (coefficients: −3×2=−6, exponents: 1+1=2)
→ −3x · (−1) = +3x (neg × neg = pos)
= −6x² + 3x
Worked Example — Monomial × Trinomial

Multiply: −4x(x² + 2x − 1)

−4x(x² + 2x − 1)
→ Distribute −4x to all three terms
→ −4x · x² = −4x³
→ −4x · 2x = −8x²
→ −4x · (−1) = +4x (neg × neg = pos)
= −4x³ − 8x² + 4x

Binomial × Binomial — The Box Method

Draw a 2×2 box. Put one binomial across the top, one down the left side. Multiply each pair and fill in the four cells. Then combine the like terms from the diagonal cells.

Worked Example — (x + 3)(x + 2)

Draw a 2×2 box. Put the terms of the first binomial across the top, the second down the left side. Multiply each pair.

x
+3
x
x²
+3x
+2
+2x
+6
→ The shaded cells are like terms — combine them: 3x + 2x = 5x
= x² + 5x + 6
Worked Example — (x − 4)(x + 3) — with negatives
x
−4
x
x²
−4x
+3
+3x
−12
→ Combine shaded cells: −4x + 3x = −x
= x² − x − 12
Common mistakes:
• Adding exponents instead of multiplying coefficients — 3x · 4x ≠ 7x²
• Forgetting to distribute to every term
• Sign errors — neg × neg = positive
• Not combining the like terms in the middle cells of the box
🎯 Test Strategy — Use the Answer Choices as Checkpoints

Before you start multiplying, look at the answer choices. The structure of the answers tells you what to expect — and lets you eliminate wrong answers as you work.

1.Check the degree first. What is the highest exponent in the answer? If you're multiplying x² · x³, the answer must have x⁵. Eliminate any choice that doesn't.
2.Check the sign of the leading term. If both factors are negative, the leading term is positive. Eliminate choices with the wrong sign at the front.
3.Work out the middle term. For binomial × binomial, the middle term comes from combining the two diagonal cells. Compare to your remaining choices.
4.Check the constant last. Multiply the two constant terms. If it doesn't match the one remaining answer, recheck your signs.
Reference
GED Formula Sheet
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📋 Open Formula Sheet

✏️ Practice Questions

Bank 1 — Monomial × Monomial
Questions are random — answer as many as you like
You've answered 5 questions. Keep going or check your score.
Bank 2 — Monomial × Polynomial
Questions are random — answer as many as you like
You've answered 5 questions. Keep going or check your score.
Bank 3 — Binomial × Binomial (Box Method)
Questions are random — answer as many as you like
You've answered 5 questions. Keep going or check your score.
Up Next in Algebra Part 1
Scale Factors & Proportions
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