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Vesna [10]
3 years ago
8

How would the expression x^3-8 be written using difference of cubes

Mathematics
2 answers:
antoniya [11.8K]3 years ago
6 0

a^3 - b^3 = (a - b)(a^2 + ab + b^2)

x^3 - 8 =

= x^3 - 2^3

= (x - 2)(x^2 + x(2) + 2^2)

= (x - 2)(x^2 + 2x + 4)

Answer: (x - 2)(x^2 + 2x + 4)

ludmilkaskok [199]3 years ago
4 0

we can use formula

a^3-b^3=(a-b)(a^2+ab+b^2)

we can compare

we get

a=x

b=2

now, we can plug that in formula

and we get

x^3-2^3=(x-2)(x^2+2x+2^2)

now, we can simplify it

x^3-8=(x-2)(x^2+2x+4)...........Answer

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Which value from the set {3, 8, 9, 14} makes the equation true?
garik1379 [7]

the answer would be 8.

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7 0
3 years ago
HELP 40 POINTS
Tom [10]
Answer: the function g(x) has the smallest minimum y-value.


Explanation:


1) The function f(x) = 3x² + 12x + 16 is a parabola.


The vertex of the parabola is the minimum or maximum on the parabola.


If the parabola open down then the vertex is a maximum, and if the parabola open upward the vertex is a minimum.


The sign of the coefficient of the quadratic term tells whether the parabola opens upward or downward.


When such coefficient is positive, the parabola opens upward (so it has a minimum); when the coefficient is negative the parabola opens downward (so it has a maximum).


Here the coefficient is positive (3), which tells that the vertex of the parabola is a miimum.


Then, finding the minimum value of the function is done by finding the vertex.

I will change the form of the function to the vertex form by completing squares:

Given: 3x² + 12x + 16

Group: (3x² + 12x) + 16
Common factor: 3 [x² + 4x ] + 16
Complete squares: 3[ ( x² + 4x + 4) - 4] + 16
Factor the trinomial: 3 [(x + 2)² - 4] + 16
Distributive property: 3 (x + 2)² - 12 + 16
Combine like terms: 3 (x + 2)² + 4

That is the vertex form: A(x - h)² + k, whch means that the vertex is (h,k) = (-2, 4).


Then the minimum value is 4 (when x = - 2).


2) The othe function is <span>g(x)= 2 *sin(x-pi)
</span>

The sine function goes from -1 to + 1, so the minimum value of sin(x - pi) is - 1.


When you multiply by 2, you just increased the amplitude of the function and obtain the new minimum value is 2 (-1) = - 2


Comparing the two minima, you have 4 vs - 2, and so the function g(x) has the smallest minimum y-value.

7 0
3 years ago
Max Steel drives his 1969 Mustang 15 miles per hour. If there are 5280 feet in one mile and 60 seconds in one minute, how many f
shutvik [7]

Answer:

22 feet per second

Step-by-step explanation

15x5280=79,200

79,200/60=1320 feet per minute since 60 minutes per hour

1320/60=22 feet per second since 60 seconds per minute

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3 years ago
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4(5x + 12) simplified = 20x + 48
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The vertex form is y=(x-4)^2-1
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