Exercise
$\left(\:+23\right)-\:\left(+8\right)\:$
Step-by-step Solution
1
Factor the sum or difference of cubes using the formula: $a^3\pm b^3 = (a\pm b)(a^2\mp ab+b^2)$
$\left(\sqrt[3]{+23}+\sqrt[3]{8}\right)\left(\sqrt[3]{\left(+23\right)^{2}}-\sqrt[3]{+23}\sqrt[3]{8}+\sqrt[3]{\left(8\right)^{2}}\right)$
2
Calculate the power $\sqrt[3]{8}$
$\left(\sqrt[3]{+23}+2\right)\left(\sqrt[3]{\left(+23\right)^{2}}-\sqrt[3]{+23}\sqrt[3]{8}+\sqrt[3]{\left(8\right)^{2}}\right)$
3
Calculate the power $\sqrt[3]{8}$
$\left(\sqrt[3]{+23}+2\right)\left(\sqrt[3]{\left(+23\right)^{2}}- 2\sqrt[3]{+23}+\sqrt[3]{\left(8\right)^{2}}\right)$
4
Multiply $-1$ times $2$
$\left(\sqrt[3]{+23}+2\right)\left(\sqrt[3]{\left(+23\right)^{2}}-2\sqrt[3]{+23}+\sqrt[3]{\left(8\right)^{2}}\right)$
5
Calculate the power $\sqrt[3]{\left(8\right)^{2}}$
$\left(\sqrt[3]{+23}+2\right)\left(\sqrt[3]{\left(+23\right)^{2}}-2\sqrt[3]{+23}+4\right)$
Final answer to the exercise
$\left(\sqrt[3]{+23}+2\right)\left(\sqrt[3]{\left(+23\right)^{2}}-2\sqrt[3]{+23}+4\right)$