multiply. $$ 3 x y\left(2 x^{2}+6 x y-9 y\right) $$

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UpStudy AI · Accepted Answer

1. Distribute the multiplication of $$3xy$$ over each term inside the parentheses:
   $$
   3xy\left(2x^2 + 6xy - 9y\right) = 3xy\cdot 2x^2 + 3xy\cdot 6xy + 3xy\cdot (-9y)
   $$

2. Multiply term by term:
   - For the first term:
     $$
     3xy \cdot 2x^2 = 6x^3y
     $$
   - For the second term:
     $$
     3xy \cdot 6xy = 18x^2y^2
     $$
   - For the third term:
     $$
     3xy \cdot (-9y) = -27xy^2
     $$

3. Combine the results to obtain the simplified expression:
   $$
   6x^3y + 18x^2y^2 - 27xy^2
   $$
The simplified expression is $$6x^3y + 18x^2y^2 - 27xy^2$$.

multiply. \( 3 x y\left(2 x^{2}+6 x y-9 y\right) \)

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