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Distribution Property using variables and exponents

by Edward
(Louisiana)











































(a^2+b^3)(a^4+b^3)

Can anyone help me with this problem, I'm kind of having a little trouble with it?

Comments for Distribution Property using variables and exponents

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Mar 25, 2010
Distributive Property
by: Staff

Distribution Property using variables and exponents



The problem


(a^2+b^3)(a^4+b^3)

Can anyone help me with this problem, I'm kind of having a little trouble with it?



The solution


The easiest way to multiply these two expressions together is the vertical format:

Line up one expression under the other, just as you would when multiplying two numbers together:

For example, if you are multiplying 236 by 409, you would write:

236
x 409
--------

For your problem, multiplying (a^2 + b^3) by (a^4 + b^3), you would write:


a^2 + b^3
x a^4 + b^3
-------------------

now, multiply:



(a^4) (a^2) = a^6

(a^4) (b^3) = a^4b^3

(a^2) (b^3) = a^2b^3

(b^3) (b^3) = b^6


a^2 + b^3
x a^4 + b^3
-------------------

a^6 + a^4b^3
a^2b^3 + b^6
------------------------------------------
a^6 + a^4b^3 + a^2b^3 + b^6

The final answer is: a^6 + a^4b^3 + a^2b^3 + b^6
(none of the terms can be combined)

This technique is also covered on the following web page:

http://www.solving-math-problems.com/distributive-property.html








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