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

find the product of the monomial and the polynomial:

1. xyz*(2x+3y^2-3z^2)

2. 4x^3y^3*(3x^3-7xy^2+2xy-y)

3. -4m n^3*(-3m^2n+12m n^2-6m+7n^2

as John said, just use the distributive property

xyz*(2x+3y^2-3z^2)
= (xyz)(2x) + (xyz)(3y^2) + (xyz)(-3z^2)
= 2x^2yz + 3xy^3z - 3xyz^3

do the others in like wise

Did you know?

In mathematics, finding the product of a monomial and a polynomial involves multiplying each term of the polynomial by the monomial. This can be done by using the distributive property. By simplifying the expressions, we can determine the final product. So, let's break it down: 1. To find the product of xyz and (2x+3y^2-3z^2), we distribute the monomial to each term of the polynomial: xyz * 2x = 2x^2yz xyz * 3y^2 = 3xy^3z xyz * -3z^2 = -3xyz^3 The final product is 2x^2yz + 3xy^3z - 3xyz^3. 2. For the expression 4x^3y^3 * (3x^3-7xy^2+2xy-y), we apply the distributive property as follows: 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 simplified product is 12x^6y^3 - 28x^4y^5 + 8x^4y^4 - 4x^3y^4. 3. In the case of -4mn^3 * (-3m^2n + 12mn^2 - 6m + 7n^2), we use the distributive property to multiply: -4mn^3 * -3m^2n = 12m^3n^4 -4mn^3 * 12mn^2 = -48m^2n^5 -4mn^3 * -6m = 24m^2n^3 -4mn^3 * 7n^2 = -28mn^5 The resultant product can be simplified as 12m^3n^4 - 48m^2n^5 + 24m^2n^3 - 28mn^5. Remember, when multiplying a monomial and a polynomial, distribute the monomial to each term of the polynomial and simplify the resultant expression.