Equivalent expressions

Front

What is an equivalent expression?

Back

An equivalent expression is an expression that has the same value as another expression for all values of the variable(s) involved.

Front

How do you distribute a number across a sum in parentheses?

Back

To distribute a number across a sum, multiply the number by each term inside the parentheses. For example, 4(x + 6) becomes 4x + 24.

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What is the process of combining like terms?

Back

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. For example, 6y + 22y + y combines to 29y.

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What does it mean to factor an expression?

Back

Factoring an expression means rewriting it as a product of its factors. For example, factoring 4x + 24 gives 4(x + 6).

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac, allowing you to multiply a single term by each term in a sum.

Front

How do you simplify the expression 3x + 5 + 7x + 2?

Back

To simplify, combine like terms: 3x + 7x = 10x and 5 + 2 = 7, resulting in 10x + 7.

Front

What is the result of multiplying 7 by the expression (3a + 4b)?

Back

Multiplying 7 by (3a + 4b) using the distributive property gives 21a + 28b.

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How do you combine the terms 3a^2 and 5a^2?

Back

To combine 3a^2 and 5a^2, add their coefficients: 3 + 5 = 8, resulting in 8a^2.

Front

What is the first step in simplifying an expression with parentheses?

Back

The first step is to apply the distributive property to eliminate the parentheses by multiplying the term outside by each term inside.

Front

What is the importance of understanding equivalent expressions in algebra?

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Understanding equivalent expressions is crucial for solving equations, simplifying expressions, and performing algebraic manipulations.