Expand (4x-3y)^4 using pascal's triangle ...?

1 answer:

8 0

Using row 4:

coefficients are: 1, 4, 6, 4, 1 

a^4 + a^3b + a^2b^2 + ab^3 + b^4 

Now adding the coefficients: 

1a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + 1b^4 

Substitute a and b: 

a = 4x 

b = -3y 

1(4x)^4 + 4(4x)^3(-3y) + 6(4x)^2(-3y)^2 + 4(4x)(-3y)^3 + 1(-3y)^4 

Now simplify the above: 

256x^4 - 768x^3y + 864x^2y^2 - 432xy^3 + 81y^4

You might be interested in

Write the equation of the line passing through the points (-4,-1) and (2,8)

klio [65]

<h3>Explanation:</h3>

Calculate the slope with two given coordinate points by using rise over run.

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Let these points

$\begin{cases}(x_1, y_1) = ( - 4, - 1) \\ (x_2, y_2) = ( 2, 8) \end{cases}$

$m = \frac{8 - ( - 1)}{2 - ( - 4)} \\ m = \frac{8 + 1}{2 + 4} \Longrightarrow \frac{9}{6} \Longrightarrow \frac{3}{2} \\ m = \frac{3}{2}$

Slope-Intercept

$y = mx + b \\ m = slope \\ b = y - intercept$

Substitute the value of m in the equation.

$y = \frac{3}{2} x + b$

Substitute any coordinate points that are given or part of the graph in the equation.

$(x_, y) = ( - 4, - 1)$

$- 1 = \frac{3}{2} ( - 4) + b$

Solve the equation for b-term.

$- 1 = \frac{3}{ \cancel{2}} ( \cancel{ - 4}) + b\\ - 1 = 3( - 2) + b \\ - 1 = - 6 + b \\ - 1 + 6 = b \\ 5 = b$

Rewrite the equation by substituting the value of b in the equation.

$y = \frac{3}{2} x + 5$

<h3>Answer</h3>

$\large \boxed{y = \frac{3}{2} x + 5}$

If you have any questions related to the answer, feel free to ask via comment.

7 0

3 years ago

One weekday, the ticket sales person at a bus station asks every 10th ticket buyer if they had planned to use a laptop computer

andrew-mc [135]

From the 3100 weekday bus traveler, 310 travelers will be asked by the sales person. And for every 2.685 traveler questioned, a traveler will say yes. So there will be 115 bus travelers that will use a laptop computer while travelling.

8 0

3 years ago

Pls i need this asap

Goryan [66]

Answer:

It would have to be (C) 50.27 because 25 is too short for a diameter of 8 seeing it would be 8x4 to get 32 in which 25 is not long enough for. So the answer is C.

6 0

3 years ago

Roger wants to carpet a rectangular room with length of 8 3/4 feet and a width of 9 1/3 feet. If he has 85 square feet of carpet

Dima020 [189]

Answer:

12.66 $ft^2$