(2x+3)(4x^2-6x+9)

2 min read Jun 16, 2024

Expanding the Expression (2x+3)(4x^2-6x+9)

This expression represents the product of a binomial and a trinomial. To expand it, we can use the distributive property (also known as FOIL for binomials). Here's how it works:

1. Distribute the First Term

First, we distribute the 2x from the binomial to each term in the trinomial:

2x * 4x² = 8x³
2x * -6x = -12x²
2x * 9 = 18x

2. Distribute the Second Term

Next, we distribute the 3 from the binomial to each term in the trinomial:

3 * 4x² = 12x²
3 * -6x = -18x
3 * 9 = 27

3. Combine Like Terms

Now, we combine the terms we obtained from both distributions:

8x³ - 12x² + 18x + 12x² - 18x + 27

Notice that the -12x² and 12x² terms cancel out, and the 18x and -18x terms also cancel out.

This leaves us with:

8x³ + 27

Final Answer

Therefore, the expanded form of (2x+3)(4x^2-6x+9) is 8x³ + 27.

Important Note: This expression is a special case known as the "sum of cubes" factorization. The pattern is: (a + b)(a² - ab + b²) = a³ + b³

In our case, a = 2x and b = 3, which perfectly fits the pattern.