Math Problem Statement
Which pair of expressions are equivalent? A.3+5a+−5 and 3+a
B.2a+15(5a) and 2a+1
C.−18(−8a) and −a
D.3a+8a+(−8a) and 3a what is the answer
Solution
Let's analyze each pair of expressions step by step to determine which are equivalent:
A. and
Simplify the first expression: The second expression is .
These are not equivalent because .
B. and
Simplify the first expression: So, .
The second expression is .
These are not equivalent because .
C. and
Simplify the first expression: The second expression is .
These are not equivalent because .
D. and
Simplify the first expression: The second expression is .
These are equivalent because .
Conclusion:
The correct answer is D. and .
Do you want details or have any questions? Here are 5 related questions:
- How do you simplify algebraic expressions with like terms?
- What happens when you multiply negative numbers in algebra?
- How can we factor an expression like ?
- What are the properties of equivalent expressions?
- How do parentheses affect operations in expressions?
Tip: Always combine like terms when simplifying expressions to see equivalency.
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Math Problem Analysis
Mathematical Concepts
Algebra
Simplification of Expressions
Combining Like Terms
Multiplying Negative Numbers
Formulas
Simplification of terms
Combining like terms: a + b = c when terms are alike
Multiplication of negative numbers: (-a)(-b) = ab
Theorems
Distributive Property
Properties of Equality
Suitable Grade Level
Grades 6-8