Write the monomial to the left and the polynomial in parentheses to the right on a piece of paper.
Examine each sign before you think about multiplying the numbers. If the monomial is positive and the first term of the polynomial is negative, the result would be negative because a positive times a negative is a negative. So write the correct sign down in your answer. If a term has no sign, it's positive.
Multiply the constant in the monomial and the constant in the first term of the polynomial. Write down the answer after the sign. For example, if you're multiplying -5v(1 - v), the first term of the product would be -5v -- that is, -5v x 1.
Use the rules of exponents to multiply variables, such as "x" or "y." For example, if you have x^3 times x^2, each term has the same base (x). The product will be x^5. Add the exponents and write down the variable with its new exponent to the right of the sign and the number. Do this for each exponent that is in that term of the polynomial. If there is a variable that is only in the monomial or only in the polynomial, copy it down just as it is, with the exponent it has.
Go through all three steps for each term of the polynomial. This is the distributive property at work. For example, if your problem were -2x(3x - 7x), you would notice that the first term of the product will be negative and the second term will be positive. The answer would be -6x^2 + 14x^2.