%5E3-expand.jpeg "(2x)^3 Expand")
Expanding (2x)^3
In mathematics, expanding an expression means rewriting it in a way that eliminates parentheses and simplifies the terms. Let's explore how to expand the expression (2x)^3.
Understanding the Exponent
The exponent 3 in (2x)^3 indicates that we multiply the base (2x) by itself three times:
(2x)^3 = (2x) * (2x) * (2x)
Applying the Distributive Property
To expand the expression, we can use the distributive property of multiplication. This property states that multiplying a sum by a number is the same as multiplying each term of the sum by that number.
- First multiplication: (2x) * (2x) = 4x²
- Second multiplication: (4x²) * (2x) = 8x³
The Final Result
Therefore, the expanded form of (2x)^3 is 8x³.
Key Points
- Exponent rule: (ab)^n = a^n * b^n
- The distributive property is a fundamental tool for simplifying expressions.
Expanding expressions is a crucial skill in algebra, allowing us to manipulate equations and solve problems more efficiently. By understanding the concepts of exponents and the distributive property, we can confidently expand complex expressions like (2x)^3.