Transcript text: Expand $\left(x^{2}-9 x y\right)(2 x+5 y)$
Solution
Solution Steps
Step 1: Expand the Expression
To expand the expression \((x^{2}-9xy)(2x+5y)\), we apply the distributive property. This involves multiplying each term in the first polynomial by each term in the second polynomial.
Step 2: Perform the Multiplication
Carrying out the multiplication, we have:
\[
x^{2} \cdot 2x + x^{2} \cdot 5y - 9xy \cdot 2x - 9xy \cdot 5y
\]
This simplifies to:
\[
2x^{3} + 5x^{2}y - 18x^{2}y - 45xy^{2}
\]
Step 3: Combine Like Terms
Now, we combine the like terms:
\[
2x^{3} + (5 - 18)x^{2}y - 45xy^{2} = 2x^{3} - 13x^{2}y - 45xy^{2}
\]
Final Answer
The expanded form of the expression \((x^{2}-9xy)(2x+5y)\) is:
\[
\boxed{2x^{3} - 13x^{2}y - 45xy^{2}}
\]