Math July 13, 2026 · 8 Min Read

Multiplying Binomials Calculator – Guide & Formulas

Multiply binomials instantly using the FOIL method. Enter two binomials like (ax + b)(cx + d) and see the expanded form with step-by-step FOIL breakdown.

Multiply any two binomials instantly with our free calculator. Enter expressions like (2x + 3)(x - 5) and see the FOIL breakdown and expanded result.

Key Takeaway

Use the free Multiplying Binomials Calculator to multiply binomials instantly using the foil method. enter two binomials like (ax + b)(cx + d) and see the expanded form with step-by-step foil breakdown. Get instant results with step-by-step explanations.

How to Use the Multiplying Binomials Calculator

  1. Enter the first binomial in the form (ax + b), e.g., (2x + 3).
  2. Enter the second binomial in the form (cx + d), e.g., (x - 5).
  3. Review the expanded polynomial result.
  4. Check the step-by-step FOIL breakdown showing each multiplication.

The Formula

Multiply using FOIL: First (a·c·x²), Outer (a·d·x), Inner (b·c·x), Last (b·d). Combine like terms: (ad + bc)x.

Variable Definitions

  • a, c: Coefficients of x in each binomial
  • b, d: Constant terms in each binomial
  • FOIL: First, Outer, Inner, Last — the multiplication order
  • ac: Coefficient of the x² term (from First)
  • bd: Constant term (from Last)

Multiplying (2x + 3)(x - 5)

Expand using the FOIL method.

  1. Step 1: First: 2x × x = 2x².
  2. Step 2: Outer: 2x × (-5) = -10x.
  3. Step 3: Inner: 3 × x = 3x.
  4. Step 4: Last: 3 × (-5) = -15.
  5. Step 5: Combine: 2x² + (-10x + 3x) + (-15) = 2x² - 7x - 15.

Frequently Asked Questions

What is the FOIL method?

FOIL stands for First, Outer, Inner, Last. It is a mnemonic for multiplying two binomials: multiply the First terms, then Outer terms, then Inner terms, then Last terms, and combine like terms.

Does FOIL work for more than two binomials?

FOIL is specifically for two binomials. For multiplying three or more binomials, multiply them sequentially: first multiply two, then multiply the result by the third, and so on.

What if one binomial has a negative term?

Distribute the negative sign carefully. For (x - 3)(x + 2): First = x², Outer = 2x, Inner = -3x, Last = -6. Combine: x² - x - 6.

Can I multiply binomials with higher-degree terms?

Yes. FOIL works for any two binomials, including those with x² or x³ terms. Multiply each term in the first binomial by each term in the second, then combine like terms.

What if the binomial has coefficients on both x terms?

FOIL still applies. For (3x + 2)(4x - 1): First = 12x², Outer = -3x, Inner = 8x, Last = -2. Result: 12x² + 5x - 2.

How do I verify my multiplication?

Substitute a value for x in both the original and expanded forms. If the results match, your multiplication is correct. For example, x = 1: (2·1+3)(1-5) = 5·(-4) = -20, and 2·1² - 7·1 - 15 = -20 ✓.

What is the difference between FOIL and distribution?

FOIL is a shortcut for the distributive property applied to two binomials. It ensures every term in the first binomial multiplies every term in the second.

Can I use this for binomials with variables only?

Yes. (x + y)(x - y) = x² - y² (difference of squares). (x + y)² = x² + 2xy + y² (perfect square trinomial).