Factor 125d^(3)-t^(3) completely. Answer:

Recognize as difference of cubes: Recognize the expression as a difference of cubes. The expression 125d^(3)-t^(3) can be written as (5d)^3 - t^3, which is a difference of cubes since 125 is 5^3.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 is 5d and b is t.Substitute a and b: Substitute a and b into the formula. Using the formula from Step 2, we substitute a with 5d and b with t to get: (5d - t)((5d)^2 + (5d)(t) + t^2)Expand terms: Expand the terms in the formula. Now we expand (5d)^2 and (5d)(t): (5d - t)(25d^2 + 5dt + t^2)Write final factorized form: Write the final factorized form. The completely factorized form of the expression is: (5d - t)(25d^2 + 5dt + t^2)

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Factor
125d^(3)-t^(3) completely.
Answer:

Factor $125 d^{3}-t^{3}$ completely. $\newline$ Answer:

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Algebra 2

Evaluate rational exponents

Full solution

Q. Factor

125 d^{3}-t^{3}

completely.

\newline

Answer:

Recognize as difference of cubes: Recognize the expression as a difference of cubes. $\newline$ The expression $125d^{3}-t^{3}$ can be written as $(5d)^3 - t^3$ , which is a difference of cubes since $125$ is $5^3$ .
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, $a$ is $5d$ and $b$ is $t$ .
Substitute $a$ and $b$ : Substitute $a$ and $b$ into the formula. $\newline$ Using the formula from Step $2$ , we substitute $a$ with $5d$ and $b$ with $t$ to get: $\newline$ $(5d - t)((5d)^2 + (5d)(t) + t^2)$
Expand terms: Expand the terms in the formula. $\newline$ Now we expand $(5d)^2$ and $(5d)(t)$ : $\newline$ $(5d - t)(25d^2 + 5dt + t^2)$
Write final factorized form: Write the final factorized form. $\newline$ The completely factorized form of the expression is: $\newline$ $(5d - t)(25d^2 + 5dt + t^2)$