Questions: Expand (x^2-9xy)(2x+5y)

Expand (x^2-9xy)(2x+5y)
Transcript text: Expand $\left(x^{2}-9 x y\right)(2 x+5 y)$
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Solution

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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: \[ \boxed{2x^{3} - 13x^{2}y - 45xy^{2}} \]

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