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Use the Distributive Property to write an 1. \( x(x+3)= \) 3. \( (y-2) x= \) 5. \( 3 x-6= \) 7. \( y \cdot 3+z \cdot 3= \)

Ask by Ramirez Gibbs. in the United States
Feb 25,2025

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Answer

1. \( x(x + 3) = x^2 + 3x \) 3. \( (y - 2)x = xy - 2x \) 5. \( 3x - 6 = 3(x - 2) \) 7. \( y \cdot 3 + z \cdot 3 = 3(y + z) \)

Solution

Below are the steps using the Distributive Property: 1. x(x + 3)   Multiply x by each term inside the parenthesis:   x · x + x · 3 = x² + 3x 3. (y - 2)x   Multiply x by each term inside the parenthesis:   x · y + x · (–2) = xy – 2x 5. 3x – 6   Notice that both terms have a common factor of 3:   3x – 6 = 3(x – 2) 7. y · 3 + z · 3   Both terms have the factor 3:   3y + 3z = 3(y + z)

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Beyond the Answer

First additional information: The Distributive Property is a fundamental algebraic principle that allows us to simplify expressions by distributing a factor across terms in parentheses. For example, in the expression \( x(x + 3) \), you distribute \( x \) to both \( x \) and \( 3 \), resulting in \( x^2 + 3x \)! It's like giving each term a sprinkle of the factor! Second additional information: The real-world application of the Distributive Property can be seen in budgeting, where you might need to calculate costs. Imagine you need to buy \( x \) books for \( $3 \) each and \( y \) pencils for \( $2 \) each. By using the property, you could express your total cost as \( 3x + 2y \), making it easier to manage your budget. Who knew math could help save your pennies?

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