Simplify each expression. Justify your steps using the Commutative, Associative and Distributive Properties when necessary
8k2 + 4k - 3k2 + 3^2 - k + 5 Please let me
8k^2 + 4k - 3k^2 - k +3^2 + 5,
Combine like-terms:
5k^2 + 3k + 14,
Use Quadratic Formula:
K = (-3 +- sqrt(3^2 - 280)) / 10,
K = (-3 +- sqrt(-271)) / 10,
K = (-3 +- sqrt(271*-1)) / 10
K = (-3 +- 16.5i) / 10,
K = -0.3 + 1.65i and -0.3 - 1.65i.
To simplify the expression 8k^2 + 4k - 3k^2 + 3^2 - k + 5, we need to combine like terms. Like terms are terms that have the same variable raised to the same exponent.
First, let's group the like terms together:
(8k^2 - 3k^2) + (4k - k) + (3^2 + 5)
Now, we can simplify each group:
5k^2 + 3k + 3^2 + 5
Simplifying further:
5k^2 + 3k + 9 + 5
Finally, combining like terms:
5k^2 + 3k + 14
Now, let's justify the steps using the properties.
1. Commutative Property: This property states that the order of terms in addition or multiplication does not change the result. As we group the like terms together and rearrange them, we are using the commutative property of addition.
2. Associative Property: This property states that the grouping of terms in addition or multiplication does not change the result. When we group the like terms together, we are using the associative property of addition.
3. Distributive Property: This property states that when a number is multiplied by the sum of two or more terms, we can distribute the multiplication to each term separately. In the expression, there is no need to use the distributive property since there are no multiplication operations involved.