Question

Convert the product into a polynomial: (4x^2y+3xy-x^2)(-x^3y^2)

Answer 1

The converted polynomial is:

-4x⁵y³ - 3x⁴y³ + x³y²

Step-by-step explanation:

Distribute the terms:

a) (4x^2y) * (-x^3y^2) = -4x⁵y³

b) (3xy) * (-x^3y^2) = -3x⁴y³

c) (-x^2) * (-x^3y^2) = x³y²

Combine like terms:

-4x⁵y³ - 3x⁴y³ + x³y²

Therefore, the simplified polynomial is -4x⁵y³ - 3x⁴y³ + x³y².

Answer 2

The product is:

`(-x^3y^2)(4x^2y+3xy-x^2)`

What we have to do is to distribute the -x^3 y^2 term over the other three terms:

`-4x^5y^3-3x^4y^3+x^5y^2`

In the first term I did:

`-x^3y^2*4x^2y=-4x^5y^3`

The second term was:

`-x^3y^2*3xy=-3x^4y^3`

And finally, the third term:

`-x^3y^2*-x^2=x^5y^2`

Then the answer is:

`-4x^5y^3-3x^4y^3+x^5y^2`