OAR Math Skills: Algebraic Expressions Questions and Answers

Question 1

Simplify the following algebraic expression: 5(2x - 3y) - (4x - 7y)

Accepted Answer

6x - 8y

Answer

First, distribute the 5 into the first parenthesis: 5 * 2x = 10x and 5 * -3y = -15y. This gives 10x - 15y. Next, distribute the negative sign into the second parenthesis: -1 * 4x = -4x and -1 * -7y = +7y. This gives -4x + 7y. Now, combine the like terms: (10x - 4x) + (-15y + 7y) = 6x - 8y.

Question 2

Evaluate the expression 3a² - 4ab + b² when a = -2 and b = 5.

Accepted Answer

77

Answer

Substitute the given values for a and b into the expression: 3(-2)² - 4(-2)(5) + (5)². Follow the order of operations (PEMDAS). First, calculate the exponents: (-2)² = 4 and (5)² = 25. The expression becomes 3(4) - 4(-2)(5) + 25. Next, perform multiplication: 3(4) = 12 and -4(-2)(5) = 40. The expression is now 12 + 40 + 25. Finally, perform addition: 12 + 40 + 25 = 77.

Question 3

A small company's monthly profit is given by the expression P = 150x - (85x + 2500), where x is the number of units sold. Which of the following is a simplified expression for the monthly profit?

Accepted Answer

P = 65x - 2500

Answer

To simplify the expression P = 150x - (85x + 2500), you must first distribute the negative sign to both terms within the parentheses. This changes the expression to P = 150x - 85x - 2500. Then, combine the like terms (the terms with x): 150x - 85x = 65x. The constant term remains -2500. Therefore, the simplified expression is P = 65x - 2500.

Question 4

Which algebraic expression correctly represents the phrase 'five less than the product of a number and three'?

Accepted Answer

3x - 5

Answer

Break down the phrase. 'The product of a number and three' translates to 3x. 'Five less than' indicates that you subtract 5 from the previous part. Therefore, 'five less than the product of a number and three' is written as 3x - 5.

Question 5

Simplify the polynomial expression: (4a² + 3ab - 6b²) - (a² - 2ab + 3b²)

Accepted Answer

3a² + 5ab - 9b²

Answer

To simplify, distribute the negative sign to the second polynomial: - (a² - 2ab + 3b²) becomes -a² + 2ab - 3b². Now, rewrite the entire expression and combine like terms: (4a² - a²) + (3ab + 2ab) + (-6b² - 3b²). This simplifies to 3a² + 5ab - 9b².

OAR Test Practice Test

OAR Test Practice Test

OAR Math Skills: Algebraic Expressions Questions and Answers