%5E3-expanded.jpeg "(2x-3)^3 Expanded")
Expanding (2x - 3)^3
The expression (2x - 3)^3 represents the product of (2x - 3) multiplied by itself three times:
(2x - 3)^3 = (2x - 3) * (2x - 3) * (2x - 3)
We can expand this expression using the distributive property and some algebraic manipulations. Here's how:
1. Expand the first two factors:
(2x - 3) * (2x - 3) = 4x^2 - 6x - 6x + 9 = 4x^2 - 12x + 9
2. Multiply the result from step 1 by the third factor:
(4x^2 - 12x + 9) * (2x - 3)
Now, we distribute each term of the first expression by each term of the second expression:
= (4x^2 * 2x) + (4x^2 * -3) + (-12x * 2x) + (-12x * -3) + (9 * 2x) + (9 * -3)
3. Simplify the expression:
= 8x^3 - 12x^2 - 24x^2 + 36x + 18x - 27
4. Combine like terms:
= 8x^3 - 36x^2 + 54x - 27
Therefore, the expanded form of (2x - 3)^3 is 8x^3 - 36x^2 + 54x - 27.
Key points to remember:
- You can use the distributive property or other algebraic techniques to expand expressions like this.
- Be careful with the signs and the order of operations when performing the multiplication.
- Combining like terms simplifies the final expression.
Understanding how to expand expressions like (2x - 3)^3 is crucial in algebra and other areas of mathematics. It allows you to manipulate and solve equations more effectively.