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Expand The Following Expression Calculator

Reviewed by Calculator Editorial Team

This calculator helps you expand algebraic expressions like (a+b)(c+d) using the distributive property. Learn how to apply the FOIL method and other expansion techniques with step-by-step guidance.

How to Use This Calculator

To expand an expression using this calculator:

  1. Enter the first binomial in the first input field (e.g., (a+b))
  2. Enter the second binomial in the second input field (e.g., (c+d))
  3. Click the "Calculate" button
  4. View the expanded form and step-by-step solution

The calculator will show you the expanded form using the distributive property and provide a visual representation of the expansion process.

How the Expansion Works

Expanding expressions like (a+b)(c+d) involves applying the distributive property (also known as the FOIL method for binomials). Here's how it works:

Distributive Property

(a + b)(c + d) = a(c + d) + b(c + d)

= ac + ad + bc + bd

For more complex expressions, you can apply the distributive property repeatedly until all parentheses are removed.

Tip

When expanding expressions with more than two binomials, work from left to right, expanding one pair at a time.

Worked Examples

Example 1: Simple Binomials

Expand (x+2)(y+3)

  1. Apply the distributive property: x(y+3) + 2(y+3)
  2. Distribute x: xy + 3x + 2y + 6
  3. Combine like terms: xy + 3x + 2y + 6

Example 2: Complex Expression

Expand (a+b)(c+d)(e+f)

  1. First expand (a+b)(c+d): ac + ad + bc + bd
  2. Now expand with (e+f): (ac + ad + bc + bd)(e+f)
  3. Distribute each term: ace + acf + ade + adf + bce + bcf + bde + bdf

Frequently Asked Questions

What is the difference between expanding and simplifying?
Expanding removes parentheses by distributing multiplication, while simplifying combines like terms and reduces the expression to its simplest form.
Can I expand expressions with more than two binomials?
Yes, you can expand expressions with any number of binomials by applying the distributive property step by step.
What is the FOIL method?
FOIL is a mnemonic for the order in which you multiply binomials: First, Outer, Inner, Last.