%5E2-expand.jpeg "(2x-3)^2 Expand")
Expanding (2x-3)^2
In algebra, expanding an expression means to multiply it out to remove any parentheses or other grouping symbols. In this article, we will learn how to expand the expression (2x-3)^2.
What does the ^2 mean?
Before we dive into expanding the expression, let's quickly review what the ^2 symbol means. The ^2 symbol is called the exponentiation operator, and it means "to the power of 2". In other words, (2x-3)^2 means "the result of multiplying 2x-3 by itself".
Expanding the Expression
To expand (2x-3)^2, we need to multiply 2x-3 by itself. We can do this using the distributive property of multiplication over addition, which states that:
a(b+c) = ab + ac
In our case, a = 2x-3, b = 2x, and c = -3. So, we can write:
(2x-3)^2 = (2x-3)(2x-3)
Using the distributive property, we expand the expression as follows:
= (2x-3)(2x) - (2x-3)(3)
= 4x^2 - 6x - 6x + 9
Now, we combine like terms:
= 4x^2 - 12x + 9
Final Answer
The final answer is:
(2x-3)^2 = 4x^2 - 12x + 9
This is the expanded form of the expression (2x-3)^2.
Conclusion
Expanding algebraic expressions is an important skill to master in mathematics. By using the distributive property and combining like terms, we can expand expressions like (2x-3)^2 and simplify them to a more manageable form.
