Algebra Class: Equivalent Expressions

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Questions and Answers

What is the result of distributing the expression 3(4x + 5)?

12x + 8
7x + 15
4x + 15
12x + 15 (correct)

What is the greatest common factor (GCD) of 15 and 25?

15
1
75
5 (correct)

Which step is NOT part of determining if two expressions are equivalent?

Substituting values for the variable
Finding the GCD of the coefficients (correct)
Simplifying both expressions
Comparing the simplified results

When factoring the expression 12 + 8, what is the correct factored form?

<p>4(3 + 2) (B)</p> Signup and view all the answers

Using the order of operations, what is the result of the expression 3 + 2 * (7 - 4)?

<p>10 (A), 9 (D)</p> Signup and view all the answers

Flashcards

Distributive Property

Distributing a number outside parentheses to each term inside, multiplying them.

Factoring Out a Common Factor

Finding the greatest common factor (GCD) of numbers, placing it outside parentheses, and dividing each number by the GCD inside.

Equivalent Expressions

Expressions are equivalent if they simplify to the same value for any variable value. Follow PEMDAS/BODMAS: parentheses/brackets, exponents/orders, multiplication/division (left to right), addition/subtraction (left to right).

PEMDAS/BODMAS

The order in which operations are performed in a mathematical expression: parentheses/brackets, exponents/orders, multiplication/division (left to right), addition/subtraction (left to right).

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Checking for Equivalent Expressions

Substituting different values for the variable and simplifying both expressions. If the results are the same, they are equivalent.

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Study Notes

Generating Equivalent Expressions

When a number is outside parentheses, distribute it to everything inside.
The distributive property is used to multiply a number outside parentheses by each term inside.
This can be represented by 2(r + 3) = 2r + 2(3) = 2r + 6
Factoring out a common factor involves finding the greatest common factor (GCD) between two or more numbers.
The GCD is then placed outside the parentheses, leaving the quotient of each number by the GCD inside.
Example: 8 + 2, the GCD is 2. The factored form is 2( 8/2 + 2/2) = 2(4 + 1).
To determine if expressions are equivalent, substitute different values for the variable and simplify both expressions.
If the results are the same, the expressions are equivalent.
When simplifying expressions, follow the order of operations (PEMDAS/BODMAS): parentheses/brackets, exponents/orders, multiplication and division (from left to right), addition and subtraction (from left to right).

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Description

Test your understanding of equivalent expressions in algebra. This quiz covers the distributive property, factoring, and determining equivalence through substitution. Perfect for strengthening your algebra skills and grasping foundational concepts.