Factor 64v^(3)-1 completely. Answer:

Recognize Cubes: Recognize the expression as a difference of cubes. 64v^3 - 1 can be written as (4v)^3 - 1^3, which is a difference of cubes since both 64v^3 and 1 can be expressed as cubes of some numbers.Apply 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 = 4v and b = 1.Substitute a and b: Substitute a and b into the formula. Using the formula from Step 2, we get (4v - 1)((4v)^2 + (4v)(1) + 1^2).Expand Terms: Expand the terms in the formula. Now we expand the terms to get (4v - 1)(16v^2 + 4v + 1).Check Factorization: Check for any further factorization. The quadratic 16v^2 + 4v + 1 does not have any real roots and cannot be factored further over the real numbers. Therefore, the factorization is complete.

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Factor $64 v^{3}-1$ completely. $\newline$ Answer:

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Algebra 2

Evaluate rational exponents

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Q. Factor

64 v^{3}-1

completely.

\newline

Answer:

Recognize Cubes: Recognize the expression as a difference of cubes. $64v^3 - 1$ can be written as $(4v)^3 - 1^3$ , which is a difference of cubes since both $64v^3$ and $1$ can be expressed as cubes of some numbers.
Apply 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, $a = 4v$ and $b = 1$ .
Substitute $a$ and $b$ : Substitute $a$ and $b$ into the formula. $\newline$ Using the formula from Step $2$ , we get $(4v - 1)((4v)^2 + (4v)(1) + 1^2)$ .
Expand Terms: Expand the terms in the formula. $\newline$ Now we expand the terms to get $(4v - 1)(16v^2 + 4v + 1)$ .
Check Factorization: Check for any further factorization. $\newline$ The quadratic $16v^2 + 4v + 1$ does not have any real roots and cannot be factored further over the real numbers. Therefore, the factorization is complete.