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Chapter 0: Problem 92

Simplify each algebraic expression. $$4(5 y-3)-(6 y+3)$$

Short Answer

Expert verified
The simplified expression is \(14y - 15\).

Step by step solution

01

Apply the Distributive Property

Firstly, apply the distributive property on the first term, which results in \(4 \times 5y\) and \(4 \times -3\). This results in \(20y - 12\). Therefore, the expression becomes \(20y - 12 -(6y + 3)\).
02

Distribute the Negative Sign

Next, distribute the negative sign across the \(6y\) and \(3\) in the second set of parentheses. This changes the sign of each term within the parentheses, resulting in \(-6y - 3\). The expression now becomes \(20y - 12 - 6y - 3\).
03

Combine Like Terms

Finally, combine the terms \(20y\) and \(-6y\) to get \(14y\), and combine the terms \(-12\) and \(-3\) to get \(-15\). Thus, the fully simplified expression is \(14y - 15\).

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