2.jpeg "(5ab2)2")
(5ab2)²: Expanding the Expression
The expression (5ab²)² represents the square of a product of variables and constants. To expand this, we apply the rule of exponents: (a * b)² = a² * b²
Here's how to break it down:
- Identify the base: The base is the entire expression within the parentheses: 5ab²
- Apply the exponent: The exponent is 2, meaning we multiply the base by itself twice.
- Expand the expression:
- (5ab²)² = (5ab²) * (5ab²)
- This can be further broken down as 5 * a * b² * 5 * a * b²
- Finally, we can rearrange and group like terms: (5 * 5) * (a * a) * (b² * b²)
Simplifying the Expression:
- 5 * 5 = 25
- a * a = a²
- b² * b² = b⁴
Therefore, the expanded form of (5ab²)² is: 25a²b⁴
Key Points:
- Squaring a product: Remember that when squaring a product, each factor within the product is squared.
- Simplifying exponents: Make sure to combine like terms and simplify the expression by applying the rules of exponents.