Factor 1-125v^(3) completely. Answer:

Recognize Type of Expression: Recognize the type of expression we are dealing with. The expression 1 - 125v^3 can be seen as a difference of cubes since 1 is 1^3 and 125v^3 is (5v)^3.Apply Cubes Formula: Apply the difference of cubes formula. The difference of cubes formula is a^3 - b^3 = (a - b)(a^2 + ab + b^2). Here, a = 1 and b = 5v.Substitute Values: Substitute the values of a and b into the formula. Using a = 1 and b = 5v, we get (1 - 5v)(1^2 + 1*5v + (5v)^2).Simplify Expression: Simplify the expression. Simplify the second factor: 1^2 + 1*5v + (5v)^2 = 1 + 5v + 25v^2. So, the factored form is (1 - 5v)(1 + 5v + 25v^2).

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Math Problems

Algebra 1

Factor quadratics: special cases

Full solution

Q. Factor

1-125 v^{3}

completely.

\newline

Answer:

Recognize Type of Expression: Recognize the type of expression we are dealing with. $\newline$ The expression $1 - 125v^3$ can be seen as a difference of cubes since $1$ is $1^3$ and $125v^3$ is $(5v)^3$ .
Apply Cubes Formula: Apply the difference of cubes formula. $\newline$ The difference of cubes formula is $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$ . Here, $a = 1$ and $b = 5v$ .
Substitute Values: Substitute the values of $a$ and $b$ into the formula. $\newline$ Using $a = 1$ and $b = 5v$ , we get $(1 - 5v)(1^2 + 1\cdot5v + (5v)^2)$ .
Simplify Expression: Simplify the expression. $\newline$ Simplify the second factor: $1^2 + 1\times 5v + (5v)^2 = 1 + 5v + 25v^2$ . $\newline$ So, the factored form is $(1 - 5v)(1 + 5v + 25v^2)$ .