Simplifying Variable Expressions

Front

What is the process of simplifying a variable expression?

Back

The process of simplifying a variable expression involves combining like terms and performing any arithmetic operations to reduce the expression to its simplest form.

Front

What are like terms in an expression?

Back

Like terms are terms that have the same variable raised to the same power. For example, 3x and 5x are like terms, while 3x and 4y are not.

Front

How do you combine like terms?

Back

To combine like terms, add or subtract their coefficients while keeping the variable part the same. For example, 3x + 5x = (3 + 5)x = 8x.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac. It allows you to multiply a single term by each term inside a parenthesis.

Front

How do you apply the distributive property to simplify an expression?

Back

To apply the distributive property, multiply the term outside the parentheses by each term inside the parentheses and then combine like terms if necessary.

Front

What is a coefficient in a variable expression?

Back

A coefficient is a numerical factor that multiplies a variable. For example, in 4x, 4 is the coefficient of x.

Front

What does it mean to simplify the expression 10x + 17 - 38x + 23?

Back

To simplify this expression, combine like terms: (10x - 38x) + (17 + 23) = -28x + 40.

Front

What is the result of simplifying the expression 9r - 5 + 10r?

Back

The result is 19r - 5, obtained by combining like terms 9r and 10r.

Front

How do you simplify the expression 8(5b + 7) + 5b?

Back

First, apply the distributive property: 8 * 5b + 8 * 7 + 5b = 40b + 56 + 5b. Then combine like terms: 40b + 5b = 45b, resulting in 45b + 56.

Front

What is the simplified form of 4b + 6 - 4?

Back

The simplified form is 4b + 2, obtained by combining the constant terms 6 and -4.