What is -8/25(x-25)^2 + 32 in the standard form?

(-8 (x + -35) (x - 15))/25

Step-by-step 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:

(-8 (x + -35) (x - 15))/25

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