Simplify: $-6(-6 v+3)$
A. $8-40 v$
B. $-24 v+8$
C. $36 v-18$
D. $-5 v+30$
Answer (2)
Distribute the -6 to both terms inside the parenthesis: − 6 ∗ − 6 v + ( − 6 ) ∗ 3 .
Simplify the expression: 36 v − 18 .
Compare the simplified expression with the given options.
The correct option is C: 36 v − 18 .
Explanation
Understanding the Problem We are given the expression − 6 ( − 6 v + 3 ) and asked to simplify it. Our goal is to distribute the − 6 across the terms inside the parentheses and combine like terms to arrive at a simplified expression.
Distributing the -6 To simplify the expression, we need to distribute the − 6 to both terms inside the parentheses. This means we multiply − 6 by − 6 v and − 6 by 3 :
− 6 ( − 6 v + 3 ) = ( − 6 × − 6 v ) + ( − 6 × 3 ) Remember that multiplying two negative numbers results in a positive number.
Performing the Multiplication Now, let's perform the multiplications: − 6 × − 6 v = 36 v − 6 × 3 = − 18 So, our expression becomes: 36 v − 18
Final Answer Therefore, the simplified expression is 36 v − 18 . Comparing this with the given options, we see that it matches option C.
Examples
Simplifying expressions like this is useful in many real-world situations. For example, imagine you're buying multiple items at a store, and each item has a discount. If you have an expression representing the total cost, simplifying it can help you quickly calculate the final price. Also, in physics, simplifying expressions is crucial for solving equations related to motion, energy, and other concepts. Understanding how to manipulate and simplify algebraic expressions is a fundamental skill in mathematics and its applications.
We simplified the expression − 6 ( − 6 v + 3 ) to get 36 v − 18 . The correct choice from the options given is C: 36 v − 18 . This was accomplished using the distributive property to distribute − 6 to each term in the parentheses.
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