High School

Which choice is equivalent to the expression below when \(x \leq 0\)?

a) \(50x^3 - 25x^3 + 5x^3\)
b) \(25x^3 - 5x^3 + 2x^3\)
c) \(5x^3 - 25x^3 - 3x^3\)
d) \(50x^3 - 3x^3 + 2x^3\)

Answer :

Final answer:

The expression 50x³ - 25x³ + 5x³ is equivalent to 30x³ when x ≤ 0.

Explanation:

The expression is 50x³ - 25x³ + 5x³. When x ≤ 0, the sign of the terms will depend on the sign of x. Positive values of x will result in positive terms, and negative values of x will result in negative terms. Thus, the expression can be simplified to 30x^3, where the coefficient 30 is the sum of the coefficients of the x³ terms.

Therefore, the choice that is equivalent to the expression when x ≤ 0 is a) 50x³ - 25x³ + 5x³.