About this video
Sal finds the area of a rectangle with length 4y and width 2y. Using the commutative and associative properties he regroups 4y times 2y as (4 * 2)(y * y), giving the monomial 8y^2.
You'll be able to
- write the area of a rectangle as the product of its dimensions.
- use the commutative and associative properties to regroup a product of monomials.
- simplify 4y * 2y to 8y^2.
Key words
- monomial
- A polynomial with only one term, such as 8y^2.
- commutative property
- You can multiply numbers in any order and get the same result.
- associative property
- You can group factors in a product however you like without changing the result.
Transcript
Express the area of a rectangle with the length 4y and width 2y as a monomial. So the area of a rectangle is just the width times the height, or the base times the height. Now here, the base is 4y. So let me just write it down-- area is going to be equal to the width of the base times the height.
The width is 4y and the height here is 2y. So the area is going to be 4y times 2y. Now here we can just use the associative and the commutative properties of multiplication. So just swap the order that we do this multiplying in. Instead of multiplying 4 times y times 2 times y, we could say this is the same thing as 4 times 2 times y times y.
And of course, 4 times 2, that part right over there is just equal to 8. And then y times y, well that's just y squared. Or it's y to the first times y to the first, which is also y squared. So it becomes 8y squared. So that's the area and it's a monomial. This is a polynomial with only one term.
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