Answer:
(16 (1280 x - 4071))/25
Step-by-step explanation:
Simplify the following:
16 - (-16 (-16)×5×16 (16 - 5 x))/(5 (-5) (-5))
Hint: | Express 16/(-5)×(-16)/(-5) as a single fraction.
16/(-5)×(-16)/(-5) = (16 (-16))/(-5 (-5)):
-(-16×5×(-16×16)/(-5 (-5)) (16 - 5 x))/5 + 16
Hint: | Express 5×(-16)/5×(16 (-16))/(-5 (-5)) as a single fraction.
5×(-16)/5×(16 (-16))/(-5 (-5)) = (16 (-16) 5 (-16))/(-5 (-5) 5):
16 - (-16 (-16) 16×5)/(-5 (-5) 5) (16 - 5 x)
Hint: | Multiply 16 and -16 together.
16 (-16) = -256:
-(-16-256×5 (16 - 5 x))/(-5 (-5) 5) + 16
Hint: | Multiply -256 and 5 together.
-256×5 = -1280:
-(-16-1280 (16 - 5 x))/(-5 (-5) 5) + 16
Hint: | Multiply -1280 and -16 together.
-1280 (-16) = 20480:
16 - (20480 (16 - 5 x))/(-5 (-5) 5)
Hint: | In 20480/(-5 (-5) 5), divide 20480 in the numerator by 5 in the denominator.
5 | | 4 | 0 | 9 | 6
| 2 | 0 | 4 | 8 | 0
- | 2 | 0 | | |
| | | 4 | |
| | - | 0 | |
| | | 4 | 8 |
| | - | 4 | 5 |
| | | | 3 | 0
| | | - | 3 | 0
| | | | | 0:
16 - (4096 (16 - 5 x))/(-5 (-5))
Hint: | Multiply -5 and -5 together.
-5 (-5) = 25:
16 - (4096 (16 - 5 x))/25
Hint: | Put the fractions in 16 - ((16 - 5 x)×4096)/25 over a common denominator.
Put each term in 16 - ((16 - 5 x)×4096)/25 over the common denominator 25: 16 - ((16 - 5 x)×4096)/25 = 400/25 - (4096 (16 - 5 x))/25:
400/25 - (4096 (16 - 5 x))/25
Hint: | Combine 400/25 - (4096 (16 - 5 x))/25 into a single fraction.
400/25 - (4096 (16 - 5 x))/25 = (400 - 4096 (16 - 5 x))/25:
(400 - 4096 (16 - 5 x))/25
Hint: | Distribute -4096 over 16 - 5 x.
-4096 (16 - 5 x) = 20480 x - 65536:
(20480 x - 65536 + 400)/25
Hint: | Group like terms in 20480 x - 65536 + 400.
Grouping like terms, 20480 x - 65536 + 400 = 20480 x + (400 - 65536):
(20480 x + (400 - 65536))/25
Hint: | Evaluate 400 - 65536.
400 - 65536 = -65136:
(20480 x + -65136)/25
Hint: | Factor out the greatest common divisor of the coefficients of 20480 x - 65136.
Factor 16 out of 20480 x - 65136:
Answer: (16 (1280 x - 4071))/25
