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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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Q: Do you use the distributive property with a monomial and a polynomial?

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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.

The distributive property is not used for simplified multiplication. See http://www.algebrahelp.com/lessons/simplifying/distribution for information about how to use the distributive property to simplify other equations. 20 x 12 is already simplified, so the proper way to solve it is 12 x20 ----- 240 You could potentially factor and use the commutative property to find a simpler equation, ex. 20x12 -- break 20 into 10 and 2 10x2x12 -- multiply 2 by 12 10x24 -- multiply by 10 240

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according to commutative property both the distributive laws are equal why to use two distributive laws

A monomial is a special case of a polynomial which contains only one term. To identify a particular term of a polynomial (in x), we use the name associated with the power of x contained in a term. 3 + √7 is a monomial of zero degree which has a special name such as a constant polynomial. Let's rewrite it as, 3x0 + (√2)x0 = (3 + √7)x0 , a monomial with an irrational coefficient = (3 + √7)(1) = 3 + √7.

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