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7nadin3 [17]
2 years ago
10

Factor completely 81x8 − 1. (9x4 − 1)(9x4 1) (3x2 − 1)(3x2 1)(9x4 − 1) (3x2 − 1)(3x2 1)(9x4 1) (3x2 − 1)(3x2 1)(3x2 1)(3x2 1).

Mathematics
1 answer:
mojhsa [17]2 years ago
4 0

Answer:

(3x^2 - 1)(3x^2 + 1)(9x^4 + 1).

Step-by-step explanation:

Using the identity for the difference of 2 squares;

a^2 - b^2 = (a - b)(a + b)  

we put a^2 = 81x^8 and b^2 = 1  giving

a = 9x^4 and b = 1, so:

81x^8 − 1 =   (9x^4 - 1)(9x^4 + 1)

Applying the difference of 2 squares to 9x^4 - 1:

= (3x^2 - 1)(3x^2 + 1)(9x^4 + 1).

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Hello!

In a function, each input has only one output. In A, three has two outputs, 4 and 5, so A is not a function.

In B, you can use something called the vertical line test to see if each x value has one y value as an output. You move an imaginary vertical line across the graph, and if it intersects with two points it is not a function. If we do this on our graph, it will not intersect two points. Therefore, B is a function.

In C, we can see that each input has one output, or there are all different inputs, so C is a function.

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I hope this helps!




6 0
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