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

*a*= -6 and

*b*= 7, then 4

*a*(3

*b*+ 5) + 2

*b*=?

- 638
- 624
- 610
- -610
- -638

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

*a*+

*b*)(

*a*–

*b*)?

*a*^{2}–*b*^{2}- (
*a*+*b*)^{2} - (
*a*–*b*)^{2} *a**b*(*a*–*b*)*a**b*(*a*+*b*)

**3. Expand the following expression:**

(2x – 20)(5x + 10)

- 10x
^{2}– 80x – 200 - 70x – 200
- 10x
^{2}– 80x + 200 - 10x
^{2}– 120x – 200

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

^{2}y + y/2 – 6x ?

- 221
- 461
- 872
- 1916

**5. If w = 7, calculate the value of the following expression:**

**8w**^{2} – 12w + (4w – 5) + 6

^{2}– 12w + (4w – 5) + 6

- 279
- 285
- 337
- 505

**6. Simplify the following expression:**

4(6 – 3)^{2} – (-2)

4(6 – 3)

^{2}– (-2)

- 34
- 38
- 42
- 48
- 62

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

- -59
- -27
- 15
- 5
- 2

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

^{2}+ 2(4 -18) + 33?

- -130
- -70
- -20
- 74

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

*x*+ 1)(7

*x*+ 10)

- 12x
^{2}+ 17x + 10 - 21x
^{2}+ 37x + 10 - 21x
^{2}+ 23x + 10 - 21x
^{2}+ 37x + 9

**10. 2(7 + 8)**^{2} – 12(6(2)) =

^{2}– 12(6(2)) =

- 119
- 225
- 306
- 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 *F*irst terms, then the *O*uter terms, the *I*nner terms, and finally the *L*ast terms are figured in sequence of multiplication. As a result, (a+b)(a-b)=a^{2}-ab+ba-b^{2}. Since *ab* is equal to *ba*, the middle terms cancel out each other which leaves a^{2}-b^{2}.

**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) = 10x^{2 }+ 20x – 100x – 200

Then, combine like terms to simplify the expression:

10x^{2 }– 80x – 200

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

3x^{2}y + 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.

8w^{2} – 12w + (4w – 5) + 6 = 8*7^{2} – 12(7) + (47 – 5) + 6

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

87^{2} – 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) = 21x^{2} + 30x + 7x + 10

Combine like terms to get the answer:

21x^{2} + 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.