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Question 554481: When multiplying two polynomials, what fundamental property do you use repeatedly?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the distributive property.
if a + b + c is a polynomial and d + e + f + g is another polynomial, then when you multiply (a + b + c) by (d + e + f + g), you are using the distributive property.
after the multiplication is complete you would combine like terms.
for that you are using the asociative and commutative properties.
an example:
(x + 3) * (x + 7)
using the distributive property, you get:
x^2 + 7x + 3x + 21
using the associative property, you get:
x^2 + (7x + 3x) + 21
combine like terms gets you:
x^2 + 10x + 21
in this case you did not need the commutative property, but in other cases you would make use of that as well.
that property is the one that states:
a + b + c + d equals a + d + c + b = a + c + b + d or any order you need to put them in.
an example of both the commutative and associative property would be:
x^2 + 7x - 3x^2 + 5x
you use the commutive property to make this:
x^2 - 3x^2 + 7x + 5x
you use the associative property to make this:
(x^2 - 3x^2) + (7x + 5x)
you then combine like terms to get:
-2x^2 + 12x
bottom line is you will probably make use of all the algebraic operation properties at some point or another depending on what you need to do to solve a problem, but one of the main properties in the multiplication of polynomials is the use of the distributive property.
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