Answer:
20) A = -100, B = 6, C = -6, D = 32
21) A = -21, B = 2, C = 18, D = 74
22) A = -36, B = -3060, C = -2133, D = 0
23) A = 4, B = 3, C = 20, D = 12
Step-by-step explanation:
20)
A) Move the negative one from the denom
-1 * (6 + 4)^2
Rewrite
-(6 + 4)^2
Add 6 and 4
-10^2
Raise 10 to the power of 2
-1 * 100
-100
B) Simplify the numerator
Add 6 and 0
6^2/6 = 36/6 (Raised 6 to the power of 2)
36/6 = 6
C) Same thing as B
6^2/-6 > 36/-6 > -6
D) Same concept as B/C
Add 6 and 2
8^2/2 > Raise to the second power > 64/2 = 32
D) Same concept as previous problems
(6 + 2)^2.2 > 8^2.2 > Raise power > 64/2 > 32
21)
A) Simpify -3^2 + 2 (-3) - 6
-1 * 9 + 2 (-3) - 6 [3 raised to the power of 2]
Multiply
-9 + 2 (-3) - 6
Multiply again
-9 - 6 - 6
-15 - 6
-21
B) Raise 2 to the power of 2
4 + 2(2) - 6
Multiply
4 + 4 - 6
8 - 6
2
C) Same concept as A and B
16 + 2(4) - 6
16 + 8 - 6
24 - 6
18
D) Same concept as prior answers
64 + 2 (8) - 6
64 + 16 - 6
80 - 6
74
22)
A) -3(2) (2^2 + 2)
Multiply -3 by 2
-6(2^2 + 2)
Raise power
-6(4 + 2)
Add 4 and 2
-6 * 6 = -36
B) Same as A
Multiply -3(10)(10^2 + 2)
-30(10^2 + 2)
Raise power
-3(100 + 2)
-30 * 102
-3060
C) Multiply then simplify so...
-3(-9)(-9^2 +2)
27 (-9^2 + 2)
Raise power
27 (-1 * 81 + 2)
Multiply
27 (-81 + 2)
27 * -79
-2133
D) This one is easy since anything by 0 is zero but either way
0(0^2 + 2)
0(0 + 2)
0 * 2
0
23)
A) 2(4^2 + -2)/7
Simplify the numerator 2(16 - 2)/7
Subtract
2 * 14/7
Multiply
28/7 > 4
B) Cancel common factors
Factor 2 from 6
2(3^2 + 0)/2 * 3
3^2 + 0/3
Simplify the numerator
Raise the power to do so
9 + 0/3
9/3 > 3
C) 2(-1^2 - 9)/-1
Simplify by moving the negative and then rewriting...
-1 * (2(-1^2 - 9)
-(2(-1^2 - 9)
One to any power is one as you should know
(-2(-1 * 1 - 9)
Multiply
-(2(-1 - 9)
Simplify further by subtraction [ 9 from - 1 ]
-(2 * -10)
Multiply again
- -20
Multiply again -1 by -20
20
D) So... 2(-5^2 + -5)/-5
Lets cancel the common factors by factoring.
So -1 out of -5^2
2(-(5^2) - 5/-5
Rewrite -5 as -1(5)
2(-5(5^2) - 1(5))/-5
Factor -1 out of -(5^2) - 1(5)
2(-(5^2 +5))/-5
Rewrite....
2(-1(5^2 + 5))/-5
Factor 5 out...
5(2(-1(5+1)))/-5
Move the ngeative
-1 * (2(-1(5+1)))
Rewrite
-(2(-1(5+1)))
Add 5 and 1
(-2(-1 * 6)
Multiply
-(2 * -6)
- -12
Multiply -1 by -12
12
