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### Course: Algebra (all content)>Unit 10

Lesson 5: Multiplying monomials by polynomials

# Multiplying monomials by polynomials challenge

Sal finds the values of coefficients c, d, and f that make -2y(y²+cy-3)=dy³+12y²+fy true for all y-values.

## Want to join the conversation?

• Can we solve for `c` algebraically?
• Technically yes - however on its own, you would not reveal much. Remember that equations are about balancing. So if you isolated C = __ then that blank has to contain everything else in the equation.
So if you end up with something like "c = (dy^3 + 2y^3 12y^2 + fy - 6y) / 2y^2"
It doesn't really do you much good, since you can't simplify that much further and you still end up with multiple coefficients and exponents of y that you can't do anything with - even if you already know what c, d, and f equal.
• Why do we know that each of the terms are equal to their corresponding terms?
• I am late but...

In this equation we were always multiplying the same variable by a coefficient. Because the exponents and variables match, the only way that the problem would come out correct (within reason) would be if the coefficients also match.
• What would happen if it was (-2y^2+cy-3)
• Andy,
It would be the same. Just open the bracket and continue working.
Hope this helps
• hi my doubt is that whenever i try to solve questions like these i always go wrong in the answer like find a , b . i get the constant correct but i mess up in the sign of it like ist it positive or negative.need it asap
• Sounds like you need to practice multiplying signed numbers. The basic rules are:
positive * positive = positive
positive * negative = negative
negative * positive = negative
negative * negative = positive.

Note: You know you have an issue with getting the sign correct. So, when you think you are done multiplying, go back and recheck your signs. It takes very little effort, but finding and fixing the errors as you go will help you get a better answer.
• _ love this video, it helped me to better understand how to use the distributive properties
• I don’t get it . -2y and y^2 are not like terms so why do we have to combine them
(1 vote)
• Combining like terms is what we do when we add / subtract. Yes, -2y and y^2 are unlike terms, so they can't be added/subtracted. But, the problem in the video is multiplication, not addition. We can always multiply: -2y(y^2) = -2y^3

Hope this helps.