Exercise
$\frac{m^7-n^7}{m^3+n^3}$
Step-by-step Solution
Learn how to solve factorization problems step by step online. Simplify the expression (m^7-n^7)/(m^3+n^3). Factor the sum or difference of cubes using the formula: a^3\pm b^3 = (a\pm b)(a^2\mp ab+b^2). Simplify \sqrt[3]{m^3} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 3 and n equals \frac{1}{3}. Simplify \sqrt[3]{n^3} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 3 and n equals \frac{1}{3}. Simplify \sqrt[3]{\left(m^3\right)^{2}} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 3 and n equals \frac{2}{3}.
Simplify the expression (m^7-n^7)/(m^3+n^3)
Final answer to the exercise
$\frac{m^7-n^7}{\left(m+n\right)\left(m^{2}-mn+n^{2}\right)}$