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Exercise

$\left(3x^2-7\right)^4$

Step-by-step Solution

1

Expand the binomial $\left(3x^2-7\right)^4$

$\left(3x^2\right)^4-28\left(3x^2\right)^3+294\left(3x^2\right)^2-4116x^2+2401$
2

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

$81x^{8}-28\cdot 27x^{6}+294\cdot 9x^{4}-4116x^2+2401$
3

Multiply $-28$ times $27$

$81x^{8}-756x^{6}+294\cdot 9x^{4}-4116x^2+2401$
4

Multiply $294$ times $9$

$81x^{8}-756x^{6}+2646x^{4}-4116x^2+2401$

Final answer to the exercise

$81x^{8}-756x^{6}+2646x^{4}-4116x^2+2401$

Try other ways to solve this exercise

  • Choose an option
  • Product of Binomials with Common Term
  • FOIL Method
  • Find the integral
  • Find the derivative
  • Factor
  • Integrate by partial fractions
  • Integrate by substitution
  • Integrate by parts
  • Integrate using tabular integration
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Main Topic: Special Products

Special products is the multiplication of algebraic expressions that follow certain rules and patterns, so you can predict the result without necessarily doing the multiplication.

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