GUYS PLEASE HELP!!!! URGENT!!!! 20 POINTS!! PLEASE I AM DESPERAT!!

all you do is multiply the coefficients (the numbers out in front) and when multiplying exponents you keep the base and add the exponents.)

You are using distributive law to multiply the monomial times each part of the binomial
3. -4m n^3*(-3m^2n+12m n^2-6m+7n^2
The first part of the answer is 12m^3 n^4
if there is no exponent like on m assume it is 1.

I should have said polynomial instead of binomial.

thx so much, but whats the answer?

To find the product of a monomial and a polynomial, you need to use the distributive property. This property states that you need to multiply each term in the polynomial by the monomial. Let's go through each question step by step:

1. xyz * (2x + 3y^2 - 3z^2)
To find the product, multiply the monomial xyz by each term in the parentheses:
xyz * 2x = 2xyz^2
xyz * 3y^2 = 3xyz^2y^2
xyz * -3z^2 = -3xyz^3

So the product of xyz and (2x + 3y^2 - 3z^2) is 2xyz^2 + 3xyz^2y^2 - 3xyz^3.

2. 4x^3y^3 * (3x^3 - 7xy^2 + 2xy - y)
Again, use the distributive property to multiply each term in the parentheses by the monomial:
4x^3y^3 * 3x^3 = 12x^6y^3
4x^3y^3 * -7xy^2 = -28x^4y^5
4x^3y^3 * 2xy = 8x^4y^4
4x^3y^3 * -y = -4x^3y^4

The product of 4x^3y^3 and (3x^3 - 7xy^2 + 2xy - y) is 12x^6y^3 - 28x^4y^5 + 8x^4y^4 - 4x^3y^4.

Note that in both examples, you need to apply the commutative property to ensure that the terms in the final expression are in the correct order.