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Distributive property and negative monomial

Give an example of using the distributive property for a negative monomial times a trinomial with different signs on the terms[for example:-3x(2xy+3y-2x)] and show each step of the distribution. Why do you think many students make sign errors on this type of problem? What would be your advice to a student who has trouble with signs?

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Let us take example

-4y(3yz - z + x)

Use distribution property, we will get

(-4y)(3yz) -(-4y)z + (-4y)x

= -12y^2 z + ...