Factor m^(3)+125 completely. Answer:

Identify Type and Technique: Identify the type of expression and the appropriate factoring technique. The expression m^3 + 125 is a sum of cubes since both m^3 and 125 are perfect cubes (m^3 is the cube of m and 125 is the cube of 5). The sum of cubes can be factored using the formula a^3 + b^3 = (a + b)(a^2 - ab + b^2).Apply Sum of Cubes Formula: Apply the sum of cubes formula to the expression m^3 + 125. Let a = m and b = 5, since m^3 = (m)^3 and 125 = 5^3. Using the formula, we get: m^3 + 125 = (m + 5)(m^2 - m*5 + 5^2).Simplify Factored Expression: Simplify the factored expression. m^3 + 125 = (m + 5)(m^2 - 5m + 25). This is the completely factored form of the expression m^3 + 125.

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Math Problems

Algebra 1

Factor quadratics: special cases

Full solution

Q. Factor

m^{3}+125

completely.

\newline

Answer:

Identify Type and Technique: Identify the type of expression and the appropriate factoring technique. $\newline$ The expression $m^3 + 125$ is a sum of cubes since both $m^3$ and $125$ are perfect cubes ( $m^3$ is the cube of $m$ and $125$ is the cube of $5$ ). $\newline$ The sum of cubes can be factored using the formula $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$ .
Apply Sum of Cubes Formula: Apply the sum of cubes formula to the expression $m^3 + 125$ . Let $a = m$ and $b = 5$ , since $m^3 = (m)^3$ and $125 = 5^3$ . Using the formula, we get: $m^3 + 125 = (m + 5)(m^2 - m\cdot 5 + 5^2)$ .
Simplify Factored Expression: Simplify the factored expression. $\newline$ $m^3 + 125 = (m + 5)(m^2 - 5m + 25)$ . $\newline$ This is the completely factored form of the expression $m^3 + 125$ .