If you want to multiply the monomial by the polynomial, yes. In that case, you have to multiply the monomial by every term of the polynomial. For example:
a (b + c + d) = ab + ac + ad
More generally, when you multiply together two polynomials, you have to multiply each term in one polynomial by each term of the other polynomial; for example:
(a + b)(c + d) = ac + ad + bc + bd
All this can be derived from the distributive property (just apply the distributive property repeatedly).
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Oh, the Distributive Property is a wonderful friend when it comes to sentences! Imagine you have a sentence like "I have 3 apples and 2 oranges." You can use the Distributive Property to rewrite it as "I have 3 apples and I have 2 oranges." It helps you break down and simplify sentences to make them easier to understand. Just like adding happy little trees to a painting, the Distributive Property adds clarity and beauty to your sentences.
12*56 Use the distributive property on 12: (10+2)*56 = 10*56 + 2*56 Use the distributive property on 56 twice: 10*(50+6) + 2*(50+6) = 10*50 + 10*6 + 2*50 + 2*6 = 500 + 60 + 100 + 12 = 672
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The property that multiplication is distributive over addition means that a*(b+c) = (a*b) + (a*c) The usufulness of this property can be illustrated by the following example: 8*(102) = 8*(100+2) = (8*100) + (8*2) = 800 + 16 = 816. So if you split 102 into 100 and 2, and then use the distributive property, you do not need to work with a large number such as 102.
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