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

Recognize as difference of cubes: Recognize the expression as a difference of cubes. The given expression is 125v^3 - c^3. We can see that 125 is a cube (5^3) and v^3 and c^3 are also cubes. So, the expression is a difference of cubes which can be factored using the formula a^3 - b^3 = (a - b)(a^2 + ab + b^2).Identify 'a' and 'b': Identify 'a' and 'b' in the formula for the difference of cubes. In the expression 125v^3 - c^3, we can identify 'a' as 5v (since 5v^3 = 125v^3) and 'b' as c (since c^3 = c^3).Apply formula: Apply the difference of cubes formula. Using the formula from Step 1 and the values from Step 2, we get: 125v^3 - c^3 = (5v)^3 - c^3 = (5v - c)((5v)^2 + (5v)(c) + c^2).Expand and simplify: Expand and simplify the terms in the factorization. Now we need to calculate (5v)^2, (5v)(c), and c^2: (5v)^2 = 25v^2, (5v)(c) = 5vc, c^2 = c^2. So the factorization becomes: (5v - c)(25v^2 + 5vc + c^2).Write final form: Write down the final factorized form. The completely factorized form of the expression is: 125v^3 - c^3 = (5v - c)(25v^2 + 5vc + c^2).

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

Factor $125 v^{3}-c^{3}$ completely. $\newline$ Answer:

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Algebra 2

Evaluate rational exponents

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Q. Factor

125 v^{3}-c^{3}

completely.

\newline

Answer:

Recognize as difference of cubes: Recognize the expression as a difference of cubes. $\newline$ The given expression is $125v^3 - c^3$ . We can see that $125$ is a cube ( $5^3$ ) and $v^3$ and $c^3$ are also cubes. So, the expression is a difference of cubes which can be factored using the formula $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$ .
Identify 'a' and 'b': Identify $a$ and $b$ in the formula for the difference of cubes. $\newline$ In the expression $125v^3 - c^3$ , we can identify $a$ as $5v$ (since $5v^3 = 125v^3$ ) and $b$ as $c$ (since $c^3 = c^3$ ).
Apply formula: Apply the difference of cubes formula. $\newline$ Using the formula from Step $1$ and the values from Step $2$ , we get: $\newline$ $125v^3 - c^3 = (5v)^3 - c^3 = (5v - c)((5v)^2 + (5v)(c) + c^2)$ .
Expand and simplify: Expand and simplify the terms in the factorization. $\newline$ Now we need to calculate $(5v)^2$ , $(5v)(c)$ , and $c^2$ : $\newline$ $(5v)^2 = 25v^2$ , $\newline$ $(5v)(c) = 5vc$ , $\newline$ $c^2 = c^2$ . $\newline$ So the factorization becomes: $\newline$ $(5v - c)(25v^2 + 5vc + c^2)$ .
Write final form: Write down the final factorized form. $\newline$ The completely factorized form of the expression is: $\newline$ $125v^3 - c^3 = (5v - c)(25v^2 + 5vc + c^2)$ .