This week in math class, I learned how to multiply binomials using the double distributive property. A binomial is an expression with two terms, such as (x+1) or (2x−4). To multiply two binomials, we distribute each term in the first binomial to each term in the second binomial, then combine like terms to arrive at the final answer.

Example 1

Problem: Multiply $(x+1)(x+3)$.

Steps:

1. Multiply $x$ by $(x+3)$:

   x(x+3)=x^2+3x

2. Multiply $1$ by (x+3):

   1(x+3)=x+3

3. Combine all the terms:

   x^2+3x+x+3=x^2+4x+3

so,  (x+1)(x+3) = $+3$.

Example 2

Problem: Multiply $(2x+5)(x-2)$.

Steps:

1. Multiply $2x$ by (x−2):

   2x(x−2)=2x^2−4x

2. Multiply $5$ by $(x-2)$:

   5(x−2)=5x−10

3. Combine all the terms:

   2x^2−4x+5x−10=2x^2+x−10

So, (2x+5)(x−2) = 2x^2+x−10

Multiplying binomials using the double distributive property involves distributing each term and combining like terms, which effectively simplifies expressions.