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Leno4ka [110]
3 years ago
9

Expand (2x -3y)^5 using the given formula.

Mathematics
1 answer:
horrorfan [7]3 years ago
3 0
(2x-3y)^5

(2x-3y)(2x-3y)(2x-3y)(2x-3y)(2x-3y)

1st and 2nd power :
(2x-3y)(2x-3y) = 2x(2x-3y)-3y(2x-3y) = 4x² - 6xy - 6xy + 9y²
= 4x² - 12xy + 9y²

3rd power:
(2x-3y)(4x² - 12xy + 9y²) = 2x(4x² - 12xy + 9y²) - 3y(4x² - 12xy + 9y²)
8x³ - 24x²y + 18xy² - 12x²y +36xy² - 27y³
8x³ - 24x²y - 12x²y + 18xy² + 36xy² - 27y³
8x³ - 36x²y + 54xy² - 27y³

4th power
(2x-3y)(8x³ - 36x²y + 54xy² - 27y³) = 2x(8x³ - 36x²y + 54xy² - 27y³) -3y(8x³ - 36x²y + 54xy² - 27y³) = 16x^4 - 72x³y + 108x²y² - 54xy³ - 24x³y + 108x²y² - 162xy³ + 81y^4
16x^4 - 72x³y - 24x³y + 108x²y² + 108x²y² - 54xy³ - 162xy³ + 81y^4
16x^4 - 96x³y + 216x²y² - 216xy³ + 81y^4

5th power
(2x-3y)(<span>16x^4 - 96x³y + 216x²y² - 216xy³ + 81y^4)
2x(</span>16x^4 - 96x³y + 216x²y² - 216xy³ + 81y^4) - 3y(<span>16x^4 - 96x³y + 216x²y² - 216xy³ + 81y^4)
= 32x^5 - 192x^4y + 432x</span>³y² - 432x²y³ + 162xy^4 - 48x^4y + 288x³y² - 648x²y³ + 648xy^4 - 243y^5

32x^5 - 192x^4y -48x^4y + 432x³y² + 288x³y² - 432x²y³ - 648x²y³ + 162xy^4 + 648xy^4 - 243y^5

32x^5 - 240x^4y + 720x³y² - 1,080x²y³ + 810xy^4 - 243y^5
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what does the slope of -1 tell you about thr relationship between lengths and widths of rectangles with perimeter 24?
NeX [460]

Using linear function concepts, the slope of -1 means that when one of the length/width is increased by 1, the other is decreased by 1.

<h3>What is a linear function?</h3>

A linear function is modeled by:

y = mx + b

In which:

  • m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
  • b is the y-intercept, which is the value of y when x = 0.

In this problem:

  • The lengths and the widths are interchangeable, that is, either can be considered as the input or as the output.
  • The slope of -1 means that when the input in increased by 1, the output is decreased by -1, that is, when one of the length/width is increased by 1, the other is decreased by 1.

You can learn more about linear function concepts at brainly.com/question/24808124

8 0
2 years ago
which function has real zeros at x = −10 and x = −6? f(x) = x2 16x 60 f(x) = x2 − 16x 60 f(x) = x2 4x 60 f(x) = x2 − 4x 60
LiRa [457]

Answer:

Option A is correct

The function x^2+16x+60 has real zeroes at x =-10 and x =-6

Explanation:

Given: The real zeroes or roots are x = -10, and x = -6

To find the quadratic function of degree 2.

x^2- (\alpha+\beta)x + \alpha\beta =0 where α,β are real roots.   ....[1]

Here, α= -10  and β= -6

Sum of the roots:

α+β =  -10+(-6) = -10-6 = -16

Product of the roots:

αβ = (-10)(-6)= 60

Substitute these value in equation [1] we have;

x^2-(-16)x+60 = x^2+16x+60

Therefore, the quadratic function for the real roots at x =-10 and x =-6 ;

x^2+16x+60

8 0
2 years ago
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There are 34 cows 22 pigs and 6 horses on a farm write a simplified ratio of pigs to all farm animals
forsale [732]
A simplified ratio would be 11:20
6 0
2 years ago
Which of the following are composite numbers check all that are true
-BARSIC- [3]

Answer:

33, 49, and 21.

Step-by-step explanation:

its 33, 49, and 21

hope this helps

4 0
2 years ago
PLZ HELP ME
Inessa05 [86]
It would be option C. :)
3 0
3 years ago
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