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  1. 1. C. 4x + 40

    2. a. - 2a + 10

    3. d. 13x - 45

    4. 2c-7d

    5. b. -2z - 12

    Step-by-step explanation:

    1.  4(x+10)  = 4x+4*10 = 4x+40

    C

    2.  -2(a - 5) = -2*a -2*-5 = -2a+10

    A

    3.  10x + 3 (x-15)

    10x + 3x -3*15

    10x+3x-45

    13x-45

    D

    4. -5(c+d) + 7c - 2d

    -5c-5d + 7c-2d

    -5c+7c -5d -2d

    2c-7d

    5.  2(2z + 4) - 2 (3z + 10)

    2*2z +2*4 -2 *3z -2*10

    4z+8 -6z-20

    4z-6z+8-20

    -2z-12

    B

  2. Explanation:

    the order of evaluation would be represented as

    ((a + (b * c)1)2 + d)3

    a. a * b - 1 + c

    b. a * (b - 1) / c mod d

    c. (a - b) / c & (d * e / a - 3)

    d. -a or c = d and e

    e. a > b xor c or d <= 17

    f. -a + b

    A:

    (a) ( ( ( a * b )1 – 1 )2 + c )3

    (b) ( ( ( a * ( b – 1 )1 )2 / c )3 mod d )4

    (c) ( ( ( a – b )1 / c )2 & ( ( ( d * e )3 / a )4 – 3 )5 )6

    (d) ( ( ( – a )1 or ( c = d )2 )3 and e )4

    (e) ( ( a > b )1 xor ( c or ( d <= 17 )2 )3 )4

    (f) ( – ( a + b )1 )2

  3. Factor the following:
    x^2 - 36
    x^2 - 36 = x^2 - 6^2:
    x^2 - 6^2
    Factor the difference of two squares. x^2 - 6^2 = (x - 6) (x + 6):
      (x - 6) (x + 6)

  4. The answers are explained below.

    Explanation:

    a.) * and + has same priority so then: ((a * b) - (1+c))

    b.) For (++c++) = ((++c)++) , prefix has high precedence.

    In remaining operators * and mod has same precedence So evaluate from left to right. ((a * (b - 1)) / (((++c)++) mod d))

    There for order of evaluation: ((a * (b - 1)) / (((++c)++) mod d))

    c.) for (d * e / a - 3), * has high priority so ((d *e) / a - 3). Now / and - have same priority so then see association from left to right. so

    And & has more priority than / so then order of evaluation: ((a - b) / (c & (((d * e) / a) - 3))

    d.) In question d, unary minus(-) has high priority then, - has high priority, then and has high priority and then or has low priority. So then order of evaluation: ((-a) or ((c = d) and e))

    e.) Here > and <= has high and same precedence then ( a > b) xor c or (d <= 17)

    now xor and or has same priority so associates from left to right.

    order of evaluation is : ( ((a > b) xor c) or (d <= 17))

    f.) uniary minus(-) has high precedence than + so order of evaluation is : ((-a) + b)

    Rewriting the expression where there are no precedence rues and the statement is given right to left associativity:

    a. c + 1 - b * a

    b. d mod (++c++) / (1 - b) * b

    c. (3 - a / e * d) & c / (b - a)

    d. e and d = c or -a

    e. 17 <= d or c xor b > a

    f. b + -a

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