Multiply Two Binomials

Multiplying Two Binomials

When you multiply two binomials, you are multiplying two expressions with two terms each, such as ((a+b)(c+d)). The goal is to distribute every term in the first binomial across every term in the second binomial, then combine like terms.

1. Use distribution carefully

Multiply each term in the first binomial by each term in the second:

• first × first
• first × second
• second × first
• second × second

For example, ((x+3)(x+5)) becomes:

• (x\cdot x = x^2)
• (x\cdot 5 = 5x)
• (3\cdot x = 3x)
• (3\cdot 5 = 15)

2. Combine like terms

Add terms with the same variable part: (x^2 + 5x + 3x + 15 = x^2 + 8x + 15)

3. Keep signs straight

If a term is negative, distribute the negative as well. For example, ((x-2)(x+7)) gives: (x^2 + 7x - 2x - 14 = x^2 + 5x - 14)

4. Check your work

A quick check is to count the four products and make sure no term was skipped. Also verify that all like terms were combined and the signs are correct.

Helpful habit

Write each product on a separate line at first. This reduces mistakes and makes the final simplification easier.