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Exercise

$81x^{12}-90x^6y^8+25y^{16}$

Step-by-step Solution

1

The trinomial $81x^{12}-90x^6y^8+25y^{16}$ is a perfect square trinomial, because it's discriminant is equal to zero

$\Delta=b^2-4ac=-90^2-4\left(25\right)\left(81\right) = 0$
2

Using the perfect square trinomial formula

$a^2+2ab+b^2=(a+b)^2,\:where\:a=\sqrt{25y^{16}}\:and\:b=\sqrt{81x^{12}}$
3

Factoring the perfect square trinomial

$\left(5y^{8}-9x^{6}\right)^{2}$

Final answer to the exercise

$\left(5y^{8}-9x^{6}\right)^{2}$

Try other ways to solve this exercise

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  • 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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