Use the distributive property to remove the parentheses. -2(-2x + 4w – 1) HELP!!
The Correct Answer and Explanation is:
To simplify the expression -2(-2x + 4w – 1) using the distributive property, multiply -2 by each term inside the parentheses: −2(−2x+4w−1)-2(-2x + 4w – 1)−2(−2x+4w−1)
Start by distributing -2 to -2x: −2⋅(−2x)=4x-2 \cdot (-2x) = 4x−2⋅(−2x)=4x
Next, distribute -2 to 4w: −2⋅(4w)=−8w-2 \cdot (4w) = -8w−2⋅(4w)=−8w
Then distribute -2 to -1: −2⋅(−1)=2-2 \cdot (-1) = 2−2⋅(−1)=2
Now combine all the results: 4x−8w+24x – 8w + 24x−8w+2
Explanation (300 words):
The distributive property is a fundamental rule in algebra that allows multiplication to be spread across terms inside parentheses. It follows the format:
a(b + c) = ab + ac. This property also works with subtraction and negative numbers.
In the expression -2(-2x + 4w – 1), the number outside the parentheses (-2) must be multiplied by every individual term inside the parentheses. This includes the variables and the constant.
Start with the first term inside the parentheses: -2x. Multiplying -2 by -2x gives 4x because the product of two negative numbers is positive. Next, multiply -2 by 4w, which results in -8w, since a negative times a positive is negative. Lastly, multiply -2 by -1, which results in +2 due to the rule that a negative times a negative is positive.
After all the multiplication is complete, write down the new expression formed by these three results: 4x – 8w + 2. There are no like terms to combine, so this is the simplified expression.
Using the distributive property is essential when simplifying expressions, especially those involving variables and constants. This method keeps expressions clear and manageable for solving equations or performing further algebraic operations. Ensuring each term inside the parentheses is multiplied correctly is crucial to avoid errors. Mastering this concept builds a strong foundation for more advanced algebra topics.
