3-expand.jpeg "(2x+1)3 Expand")
(2x+1)3 Expand: A Step-by-Step Guide
In algebra, expanding an expression like (2x+1)3 can seem daunting, but fear not! In this article, we'll break down the process into manageable steps.
Understanding the Expression
Before we dive into expanding the expression, let's understand what it means. The expression (2x+1)3 is a cube of the binomial 2x+1. To expand this expression, we need to multiply the binomial by itself three times.
Step 1: Multiply the Binomial by Itself
First, we'll multiply the binomial 2x+1 by itself:
(2x+1)(2x+1) = ?
Using the distributive property, we multiply each term in the first binomial by each term in the second binomial:
= (2x)(2x) + (2x)(1) + (1)(2x) + (1)(1)
Simplifying the expression, we get:
= 4x² + 2x + 2x + 1
Combine like terms:
= 4x² + 4x + 1
Step 2: Multiply the Result by the Binomial Again
Now, we'll multiply the result by the binomial 2x+1 again:
(4x² + 4x + 1)(2x+1) = ?
Using the distributive property once more:
= (4x²)(2x) + (4x²)(1) + (4x)(2x) + (4x)(1) + (1)(2x) + (1)(1)
Simplifying the expression, we get:
= 8x³ + 4x² + 8x² + 4x + 2x + 1
Combine like terms:
= 8x³ + 12x² + 6x + 1
The Final Answer
And that's it! We've successfully expanded the expression (2x+1)3:
(2x+1)3 = 8x³ + 12x² + 6x + 1
Now, you should be able to expand similar expressions with ease. Remember to follow the order of operations and combine like terms to get the final answer.
