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Exercise

$\left(3m^3n+2n\right)^2$

Step-by-step Solution

1

Expand the expression $\left(3m^3n+2n\right)^2$ using the square of a binomial

$(a+b)^2=a^2+2ab+b^2$
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2

Take the square of the first term: $3m^3n$

$9m^{6}n^{2}$
3

Twice ($2$) the product of the two terms: $3m^3n$ and $2n$

$12m^3n^2$
4

Take the square of the second term: $2n$

$4n^{2}$
5

Add the three results, and we obtain the expanded polynomial

$9m^{6}n^{2}+12m^3n^2+4n^{2}$

Final answer to the exercise

$9m^{6}n^{2}+12m^3n^2+4n^{2}$

Try other ways to solve this exercise

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  • 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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