Multiplying Binomials Calculator
Multiply two binomials using the FOIL method with step-by-step solutions
Binomial Multiplication Calculator
Formula
First Binomial: a₁x + a₀
Coefficient of the variable term
Constant term of the first binomial
Second Binomial: b₁x + b₀
Coefficient of the variable term
Constant term of the second binomial
Example Problems
Example 1: Basic Multiplication
Problem: Multiply (3x - 2)(x + 5)
Solution using FOIL:
- First: 3x × x = 3x²
- Outer: 3x × 5 = 15x
- Inner: -2 × x = -2x
- Last: -2 × 5 = -10
Combine: 3x² + 15x - 2x - 10 = 3x² + 13x - 10
Example 2: Negative Coefficients
Problem: Multiply (2x + 4)(-x + 3)
Solution using FOIL:
- First: 2x × (-x) = -2x²
- Outer: 2x × 3 = 6x
- Inner: 4 × (-x) = -4x
- Last: 4 × 3 = 12
Combine: -2x² + 6x - 4x + 12 = -2x² + 2x + 12
Example 3: Perfect Square
Problem: Multiply (x + 3)(x + 3) = (x + 3)²
Solution using FOIL:
- First: x × x = x²
- Outer: x × 3 = 3x
- Inner: 3 × x = 3x
- Last: 3 × 3 = 9
Combine: x² + 3x + 3x + 9 = x² + 6x + 9
FOIL Method
F - First
Multiply the first terms: a₁x × b₁x = a₁b₁x²
O - Outer
Multiply the outer terms: a₁x × b₀ = a₁b₀x
I - Inner
Multiply the inner terms: a₀ × b₁x = a₀b₁x
L - Last
Multiply the last terms: a₀ × b₀ = a₀b₀
Final Step: Combine like terms to get the quadratic expression.
Key Concepts
Binomial
A polynomial with exactly two terms (e.g., 3x + 2)
Trinomial Result
Multiplying two binomials typically results in a trinomial
Like Terms
Terms with the same variable and exponent that can be combined
Standard Form
ax² + bx + c (quadratic in descending order of powers)
Quick Tips
Remember FOIL: First, Outer, Inner, Last
Always combine like terms in the final answer
Watch signs carefully when multiplying negative terms
The result is usually a quadratic trinomial
Practice with simple examples first
Understanding Binomial Multiplication
What are Binomials?
A binomial is a polynomial expression containing exactly two terms connected by addition or subtraction. Examples include 3x + 2, x - 5, and 2y + 7.
The Distributive Property
When multiplying binomials, we use the distributive property: each term in the first binomial must be multiplied by each term in the second binomial.
(a + b)(c + d) = ac + ad + bc + bd
The FOIL Method
FOIL is a mnemonic device that helps remember how to multiply two binomials:
First Terms
Multiply the first term of each binomial
Outer Terms
Multiply the outermost terms
Inner Terms
Multiply the innermost terms
Last Terms
Multiply the last term of each binomial
Step-by-Step Process
Step 1
Apply FOIL method to multiply all term combinations
Step 2
Identify and combine like terms (same variable and exponent)
Step 3
Arrange terms in descending order of powers
Step 4
Write the final quadratic expression