We're moving into Unit 3-Polynomials today. We will be seeing and using higher order exponents than we have seen thus far. Try your hand at the following, and see what you can remember from Algebra 1:
Look for 'like terms' and combine.
Example:
Here...generally, we will put the 'highest order' (the largest exponent) of the 'first term alphabetically' in the front...so since x comes before y, and x^3 is bigger than x, that's our result.
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Question 1
1.
Simplify:
When dividing exponents, focus on the LARGER of the exponent in each like term...subtract the exponents and then include the result in the same location (numerator or denominator) of the LARGER exponent.
Examples:
(1) In the 1st example, you evaluate the x's...since there are is only one y^5, it just stays in the place it started.
(2) In the 2nd example, you evaluate both the y's and the z's. Since the larger exponent of each is located in the denominator, subtract the exponents and place the result in the denominator. The numerator just becomes a 1 in this case.
(3) One more example (here, since the x's have the same exponents, you subtract and get zero...they cancel out and go away)
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Question 2
2.
Simplify:
For a power to a power....multiply the powers:
Examples:
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Question 3
3.
Simplify:
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Question 4
4.
Simplify:
(back to some basic foiling here)
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Question 5
5.
Simplify:
(careful, since there's a + in between those binomials, don't foil...drop the parentheses and combine like terms)
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Question 6
6.
Simplify: (same issue...that's subtraction, not foiling)