Factor 125+8r^(3) completely. Answer:

Identify Factoring Type: Identify the type of factoring required for the expression 125 + 8r^3. The expression is a sum of two cubes since 125 is 5^3 and 8r^3 is (2r)^3. The sum of cubes can be factored using the formula a^3 + b^3 = (a + b)(a^2 - ab + b^2).Write in Cubes Form: Write the expression in the form of a^3 + b^3. 125 + 8r^3 = 5^3 + (2r)^3 Here, a = 5 and b = 2r.Apply Sum of Cubes Formula: Apply the sum of cubes formula to factor the expression. Using a = 5 and b = 2r in the formula a^3 + b^3 = (a + b)(a^2 - ab + b^2), we get: (5 + 2r)(5^2 - 5*2r + (2r)^2)Simplify Factored Expression: Simplify the factored expression. (5 + 2r)(25 - 10r + 4r^2)Check for Further Simplification: Check for any further factorization or simplification. The expression (5 + 2r)(25 - 10r + 4r^2) cannot be simplified further, and there are no common factors to extract.

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Algebra 1

Factor quadratics: special cases

Full solution

Q. Factor

125+8 r^{3}

completely.

\newline

Answer:

Identify Factoring Type: Identify the type of factoring required for the expression $125 + 8r^3$ . The expression is a sum of two cubes since $125$ is $5^3$ and $8r^3$ is $(2r)^3$ . The sum of cubes can be factored using the formula $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$ .
Write in Cubes Form: Write the expression in the form of $a^3 + b^3$ . $\newline$ $125 + 8r^3 = 5^3 + (2r)^3$ $\newline$ Here, $a = 5$ and $b = 2r$ .
Apply Sum of Cubes Formula: Apply the sum of cubes formula to factor the expression. $\newline$ Using $a = 5$ and $b = 2r$ in the formula $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$ , we get: $\newline$ $(5 + 2r)(5^2 - 5\cdot 2r + (2r)^2)$
Simplify Factored Expression: Simplify the factored expression. $\newline$ $(5 + 2r)(25 - 10r + 4r^2)$
Check for Further Simplification: Check for any further factorization or simplification. The expression $(5 + 2r)(25 - 10r + 4r^2)$ cannot be simplified further, and there are no common factors to extract.