Order of Operations Practice Problems

1. If a = -6 and b = 7, then 4a(3b + 5) + 2b=?

1. 638
2. 624
3. 610
4. -610
5. -638

2. Which of the following expressions is equivalent to (a + b)(a – b)?

1. a²–b²
2. (a+b)²
3. (a–b)²
4. ab(a–b)
5. ab(a+b)

3. Expand the following expression:

(2x – 20)(5x + 10)

1. 10x²– 80x – 200
2. 70x – 200
3. 10x²– 80x + 200
4. 10x²– 120x – 200

4. If x=4 and y=10, what is the value of the expression 3x²y + y/2 – 6x ?

1. 221
2. 461
3. 872
4. 1916

5. If w = 7, calculate the value of the following expression:
8w² – 12w + (4w – 5) + 6

1. 279
2. 285
3. 337
4. 505

6. Simplify the following expression:
4(6 – 3)² – (-2)

1. 34
2. 38
3. 42
4. 48
5. 62

7. Simplify the following expression: -11 – (16 – 32)

1. -59
2. -27
3. 15
4. 5
5. 2

8. What is the value of the expression -3(5)²+ 2(4 -18) + 33?

1. -130
2. -70
3. -20
4. 74

9. Expand the following expression: (3x + 1)(7x + 10)

1. 12x² + 17x + 10
2. 21x² + 37x + 10
3. 21x² + 23x + 10
4. 21x² + 37x + 9

10. 2(7 + 8)² – 12(6(2)) =

1. 119
2. 225
3. 306
4. 604

Answers and Explanations

1. D:

Substitute the given values for the variables into the expression:

4*-6 (3 * 7 + 5) + 2 * 7

Remember to use the order of operations when simplifying this expression. The acronym PEMDAS will help you remember the correct order: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.

Using order of operations, compute the expression in the parentheses first.

Remember that you must first multiply 3 by 7, and then add 5 in order to follow order of operations:

= 4 * -6(21 + 5) + 2 * 7 Next, add the values in the parenthesis.

= 4 * -6(26) + 2 * 7 Simplify by multiplying the numbers outside the parenthesis.

= -24(26) + 14 Multiply -24 by 26.

= -624 + 14 Add.

= -610

2. A. Compute the product using the FOIL method, in which the First terms, then the Outer terms, the Inner terms, and finally the Last terms are figured in sequence of multiplication. As a result, (a+b)(a-b)=a²-ab+ba-b². Since ab is equal to ba, the middle terms cancel out each other which leaves a²-b².

3. A: Use the FOIL method (first, outside, inside, and last) to get rid of the parentheses:

(2x – 20)(5x + 10) = (2x)(5x) + (2x)(10) – (20)(5x) – (20)(10) = 10x² + 20x – 100x – 200

Then, combine like terms to simplify the expression:

10x² – 80x – 200

4. B: First, substitute the given values for x and y into the expression:

3x²y + y/2 – 6x = 3(4)²*10 + 10/2 – 6(4)

Then, calculate the value of the expression:

According to the order of operations, any exponents must be evaluated first:

31610 + 10/2 – 6(4)

Then, we perform any multiplication or division in order from left to right:

480 + 5 – 24

Then, any addition or subtraction should be completed:

485 – 24 = 461

5. C: First, substitute the given value of w (w = 7) into the expression each time it appears.

8w² – 12w + (4w – 5) + 6 = 8*7² – 12(7) + (47 – 5) + 6

According to the order of operations, any calculations inside of the brackets must be done first:

87² – 12(7) + (23) + 6

Next, evaluate exponents and then perform multiplication:

849 – 12(7) + 23 + 6 = 392 – 84 + 23 + 6

Finally, perform addition and subtraction:

392 – 84 + 23 + 6 = 337

6. B: First, simplify the expression inside the parentheses: 4(3)² – (-2)

Next, simplify the exponent: 4(9) – (-2)

Then, multiply: 36 – (-2)

Finally, subtract: 36 – (-2) = 36 + 2 = 38.

7. D: Remember the Order of Operations (PEMDAS) when simplifying this expression. Simplify the expression inside the parentheses first:

-11 – (16 – 32)

-11 – (-16)

Then subtract. When subtracting a negative integer, be sure to change the negative integer into a positive and then add it to the other number:

-11 – (-16) = -11 + 16 = 5

8. B: Use the order of operations to find the value for this expression.

-3(5)² + 2(4 – 18) + 33

-3(5)² + 2(-14) + 33

-3(25) + 2(-14) + 33

-75 + (-28) + 33

-70, Choice B

9. B: Use the FOIL method (First, Outer, Inner, Last) to simplify this expression:

(3x + 1)(7x + 10) = (3x)(7x) + (3x)(10) + (1)(7x) + (1)(10) = 21x² + 30x + 7x + 10

Combine like terms to get the answer:

21x² + 37x + 10

10. C: Remember the order of operations when solving this equation. First, simplify all operations inside parentheses.

2(7 + 8)² – 12 (6(2)) = 2(15)² – 12(12)

Second, simplify any exponential expressions.

2(225) – 12(12)

Third, perform all multiplication and division as they occur in the problem from left to right.

450 – 144

Finally, perform any addition or subtraction:

450 – 144 = 306.