Answer:
(-8 (x + -35) (x - 15))/25
Explanation:
Simplify the following:
32 - (8 (x - 25)^2)/25
Hint: | Put the fractions in 32 - (8 (x - 25)^2)/25 over a common denominator.
Put each term in 32 - (8 (x - 25)^2)/25 over the common denominator 25: 32 - (8 (x - 25)^2)/25 = 800/25 - (8 (x - 25)^2)/25:
800/25 - (8 (x - 25)^2)/25
Hint: | Combine 800/25 - (8 (x - 25)^2)/25 into a single fraction.
800/25 - (8 (x - 25)^2)/25 = (800 - 8 (x - 25)^2)/25:
(800 - 8 (x - 25)^2)/25
Hint: | Factor out the greatest common divisor of the coefficients of 800 - 8 (x - 25)^2.
Factor -8 out of 800 - 8 (x - 25)^2:
(-8 ((x - 25)^2 - 100))/25
Hint: | Write 100 as a square in order to express (x - 25)^2 - 100 as a difference of squares.
(x - 25)^2 - 100 = (x - 25)^2 - 10^2:
(-8 ((x - 25)^2 - 10^2))/25
Hint: | Factor the difference of two squares.
Factor the difference of two squares. (x - 25)^2 - 10^2 = ((x - 25) - 10) ((x - 25) + 10):
(-8(x - 25 - 10) (x - 25 + 10))/25
Hint: | Group like terms in x - 25 + 10.
Grouping like terms, x - 25 + 10 = x + (10 - 25):
(-8 x + (10 - 25) (x - 25 - 10))/25
Hint: | Evaluate 10 - 25.
10 - 25 = -15:
(-8 (x - 25 - 10) (x + -15))/25
Hint: | Group like terms in x - 25 - 10.
Grouping like terms, x - 25 - 10 = x + (-25 - 10):
(-8 x + (-25 - 10) (x - 15))/25
Hint: | Evaluate -25 - 10.
-25 - 10 = -35:
Answer: (-8 (x + -35) (x - 15))/25