Question

what is the product of the polynomials (x^2y+5) (2x^2 -3y) use the distributive property. x^2y * __ + x^2y x ___+5 * ___+5 * ___. the product of the polynomial is ___

Answer 1

To find the product of the polynomials \((x^2y + 5)(2x^2 - 3y)\) using the distributive property, we will distribute each term in the first polynomial to each term in the second polynomial.

Let's break it down:

1. **Distributing \(x^2y\):**
- \(x^2y \cdot 2x^2 = 2x^{4}y\)
- \(x^2y \cdot (-3y) = -3x^{2}y^{2}\)

2. **Distributing \(5\):**
- \(5 \cdot 2x^2 = 10x^{2}\)
- \(5 \cdot (-3y) = -15y\)

Now, let's combine all the results:

- From distributing \(x^2y\): \(2x^{4}y - 3x^{2}y^{2}\)
- From distributing \(5\): \(10x^{2} - 15y\)

Combining these terms together, we have:

\[
2x^{4}y - 3x^{2}y^{2} + 10x^{2} - 15y
\]

Therefore, the product of the polynomials is:

\[
2x^{4}y - 3x^{2}y^{2} + 10x^{2} - 15y
\]

So, filling in your blanks:

- \(x^2y \cdot 2x^2 + x^2y \cdot (-3y) + 5 \cdot 2x^2 + 5 \cdot (-3y)\)
- The product of the polynomial is \(2x^{4}y - 3x^{2}y^{2} + 10x^{2} - 15y\)