Evaluating Expressions

Front

What is an expression in mathematics?

Back

An expression is a combination of numbers, variables, and operators (such as +, -, *, /) that represents a value.

Front

What does it mean to evaluate an expression?

Back

To evaluate an expression means to calculate its value by substituting variables with numbers and performing the operations.

Front

What is the order of operations in mathematics?

Back

The order of operations is a set of rules that dictates the sequence in which calculations are performed: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right), often abbreviated as PEMDAS.

Front

How do you evaluate an expression with exponents?

Back

To evaluate an expression with exponents, calculate the exponent first, then perform the other operations according to the order of operations.

Front

What is the value of 3 squared?

Back

3 squared (3^2) is 9.

Front

How do you simplify the expression 3(4)^2?

Back

First, calculate 4^2 = 16, then multiply by 3: 3 * 16 = 48.

Front

What is the result of evaluating -3^2?

Back

The result of evaluating -3^2 is -9, because the negative sign is not included in the exponent.

Front

How do you evaluate the expression -3^2 - 5(2)(-3)?

Back

First, calculate -3^2 = -9. Then calculate 5(2)(-3) = -30. Finally, combine: -9 - (-30) = -9 + 30 = 21.

Front

What is the formula for the difference of squares?

Back

The difference of squares formula is a^2 - b^2 = (a - b)(a + b).

Front

How do you evaluate the expression x^2 - (x - y)^2 * y?

Back

Substitute the values of x and y into the expression, calculate (x - y)^2, then multiply by y, and finally perform the subtraction.