Multiply the monomial and the polynomial. Assume any variable exponents represent whole numbers.
-5x2y(-11x2y4 - 12xy3 - 4)
To multiply a monomial and a polynomial, you need to distribute the monomial to each term of the polynomial. In this case, the monomial is -5x^2y and the polynomial is (-11x^2y^4 - 12xy^3 - 4).
Let's start by distributing -5x^2y to each term:
(-5x^2y) * (-11x^2y^4) = -5 * -11 * x^2 * x^2 * y * y^4 = 55x^4y^5
(-5x^2y) * (-12xy^3) = -5 * -12 * x^2 * x * y * y^3 = 60x^3y^4
(-5x^2y) * (-4) = -5 * -4 * x^2 * y = 20x^2y
Now, let's combine all the terms:
55x^4y^5 + 60x^3y^4 + 20x^2y
So, the final expression is 55x^4y^5 + 60x^3y^4 + 20x^2y.