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Exercise

$\left(c^3-d^3\right)$

Step-by-step Solution

1

Factor the difference of cubes: $a^3-b^3 = (a-b)(a^2+ab+b^2)$

$\left(c-d\right)\left(c^2+cd+\sqrt[3]{\left(d^3\right)^{2}}\right)$
2

Simplify $\sqrt[3]{\left(d^3\right)^{2}}$ 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 $\frac{2}{3}$

$\left(c-d\right)\left(c^2+cd+d^{3\cdot \left(\frac{2}{3}\right)}\right)$
3

Multiply the fraction and term in $3\cdot \left(\frac{2}{3}\right)$

$\left(c-d\right)\left(c^2+cd+d^{\frac{3\cdot 2}{3}}\right)$
4

Multiply $3$ times $2$

$\left(c-d\right)\left(c^2+cd+d^{\frac{6}{3}}\right)$
5

Divide $6$ by $3$

$\left(c-d\right)\left(c^2+cd+d^{2}\right)$

Final answer to the exercise

$\left(c-d\right)\left(c^2+cd+d^{2}\right)$

Try other ways to solve this exercise

  • Choose an option
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
  • Integrate by parts
  • Integrate using tabular integration
  • Integrate by trigonometric substitution
  • Weierstrass Substitution
  • Prove from LHS (left-hand side)
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Main Topic: Common Monomial Factor

Monomial factor is a factor which has a variable and a term with some exponents. Common monomial factor means finding the common factor from the given set of monomials.

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