(2x%2B3)(2x%2B3).jpeg "(2x+3)(2x+3)(2x+3)")
Expanding the Expression (2x+3)(2x+3)(2x+3)
This expression represents the product of three identical binomials: (2x+3). Let's break down the process of expanding it.
Step 1: Expanding the First Two Binomials
We begin by expanding the first two binomials: (2x+3)(2x+3). This is a common multiplication pattern known as the "square of a binomial":
(a + b)² = a² + 2ab + b²
Applying this pattern:
(2x + 3)² = (2x)² + 2(2x)(3) + (3)²
Simplifying, we get:
(2x + 3)² = 4x² + 12x + 9
Step 2: Multiplying the Result by (2x+3)
Now we need to multiply the result from step 1 (4x² + 12x + 9) by the remaining binomial (2x+3):
(4x² + 12x + 9)(2x + 3)
To multiply this, we can use the distributive property:
- Multiply each term in the first trinomial by the first term in the binomial (2x):
- 4x² * 2x = 8x³
- 12x * 2x = 24x²
- 9 * 2x = 18x
- Multiply each term in the first trinomial by the second term in the binomial (3):
- 4x² * 3 = 12x²
- 12x * 3 = 36x
- 9 * 3 = 27
Step 3: Combining Like Terms
Finally, we combine the like terms:
8x³ + 24x² + 18x + 12x² + 36x + 27
The final expanded form of (2x+3)(2x+3)(2x+3) is:
8x³ + 36x² + 54x + 27