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. 3+5a53 + 5a - 5 and 3+a3 + a

Simplify the first expression: 3+5a5=(35)+5a=2+5a3 + 5a - 5 = (3 - 5) + 5a = -2 + 5a The second expression is 3+a3 + a.

These are not equivalent because 2+5a3+a-2 + 5a \neq 3 + a.


B. 2a+15(5a)2a + 15(5a) and 2a+12a + 1

Simplify the first expression: 15(5a)=75a15(5a) = 75a So, 2a+15(5a)=2a+75a=77a2a + 15(5a) = 2a + 75a = 77a.

The second expression is 2a+12a + 1.

These are not equivalent because 77a2a+177a \neq 2a + 1.


C. 18(8a)-18(-8a) and a-a

Simplify the first expression: 18(8a)=144a-18(-8a) = 144a The second expression is a-a.

These are not equivalent because 144aa144a \neq -a.


D. 3a+8a+(8a)3a + 8a + (-8a) and 3a3a

Simplify the first expression: 3a+8a+(8a)=3a+(8a8a)=3a+0=3a3a + 8a + (-8a) = 3a + (8a - 8a) = 3a + 0 = 3a The second expression is 3a3a.

These are equivalent because 3a=3a3a = 3a.


Conclusion:

The correct answer is D. 3a+8a+(8a)3a + 8a + (-8a) and 3a3a.


Do you want details or have any questions? Here are 5 related questions:

  1. How do you simplify algebraic expressions with like terms?
  2. What happens when you multiply negative numbers in algebra?
  3. How can we factor an expression like 15(5a)15(5a)?
  4. What are the properties of equivalent expressions?
  5. 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