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\begin{tabular}{l} O Integers and Rational Numbers \\ Distributive property: Whole number coefficients \\ \( 8(8-v) \) \\ \hline\( \square \)\end{tabular}

Ask by Bob Salazar. in the United States
Mar 10,2025

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Answer

The simplified expression is \( 64 - 8v \).

Solution

1. We start with the expression: \[ 8(8 - v) \] 2. Apply the distributive property, which states that for any \( a \), \( b \), and \( c \), \[ a(b - c) = ab - ac \] In our case, \( a = 8 \), \( b = 8 \), and \( c = v \). 3. Multiply \( 8 \) by \( 8 \) to get: \[ 8 \times 8 = 64 \] 4. Multiply \( 8 \) by \( -v \) to get: \[ 8 \times -v = -8v \] 5. Combine the two results: \[ 8(8-v) = 64 - 8v \] 6. The simplified expression is: \[ \boxed{64 - 8v} \]

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Did you know that the distributive property is like your best friend in math? It allows you to break complicated expressions into simpler parts, making calculations much easier. For example, in \( 8(8-v) \), you can distribute the 8 by multiplying both terms inside the parentheses, leading to \( 64 - 8v \). This property applies not only to integers but also to rational numbers, making it super handy across various math topics! Now, in real-world situations, the distributive property can be incredibly useful when calculating things like costs or prices. Imagine you’re buying multiple items at different prices—by using the distributive property, you can quickly find the total cost. Just like in our expression, \( 8(8-v) \), you might simplify the cost of buying 8 shirts with a discount applied, making budgeting a breeze!

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