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Exercise

$ax^4-8axy^3$

Step-by-step Solution

1

Factor the polynomial $ax^4-8axy^3$ by it's greatest common factor (GCF): $ax$

$ax\left(x^{3}-8y^{3}\right)$
2

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

$ax\left(x-\sqrt[3]{8y^{3}}\right)\left(x^2+x\sqrt[3]{8y^{3}}+\sqrt[3]{\left(8y^{3}\right)^{2}}\right)$
3

The power of a product is equal to the product of it's factors raised to the same power

$ax\left(x- 2y\right)\left(x^2+2xy+4\sqrt[3]{\left(y^{3}\right)^{2}}\right)$
4

Multiply $-1$ times $2$

$ax\left(x-2y\right)\left(x^2+2xy+4\sqrt[3]{\left(y^{3}\right)^{2}}\right)$
5

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

$ax\left(x-2y\right)\left(x^2+2xy+4y^{2}\right)$

Final answer to the exercise

$ax\left(x-2y\right)\left(x^2+2xy+4y^{2}\right)$

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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