7×65 7×(60+5)
(7×60) (7×5)
(420)+(35)
The answer is 455
Answer:
![(7C4) (2x)^4 (-y)^{7-4}](https://tex.z-dn.net/?f=%20%287C4%29%20%282x%29%5E4%20%28-y%29%5E%7B7-4%7D)
And replacing we got:
![35 (2^4) x^4 (-y)^{-3}](https://tex.z-dn.net/?f=%2035%20%282%5E4%29%20x%5E4%20%28-y%29%5E%7B-3%7D)
And then the final term would be:
![-560 x^4 y^3](https://tex.z-dn.net/?f=%20-560%20x%5E4%20y%5E3)
Step-by-step explanation:
For this case we have the following expression:
![(2x-y)^7](https://tex.z-dn.net/?f=%20%282x-y%29%5E7)
And we can use the binomial theorem given by:
![(x+y)^n =\sum_{k=0}^n (nCk) x^k y^{n-k}](https://tex.z-dn.net/?f=%20%28x%2By%29%5En%20%3D%5Csum_%7Bk%3D0%7D%5En%20%28nCk%29%20x%5Ek%20y%5E%7Bn-k%7D)
And for this case we want to find the fourth term and using the formula we have:
![(7C4) (2x)^4 (-y)^{7-4}](https://tex.z-dn.net/?f=%20%287C4%29%20%282x%29%5E4%20%28-y%29%5E%7B7-4%7D)
And replacing we got:
![35 (2^4) x^4 (-y)^{-3}](https://tex.z-dn.net/?f=%2035%20%282%5E4%29%20x%5E4%20%28-y%29%5E%7B-3%7D)
And then the final term would be:
![-560 x^4 y^3](https://tex.z-dn.net/?f=%20-560%20x%5E4%20y%5E3)
Given:
Point is T(-3,8).
To find:
The coordinates of T' after
.
Solution:
We know that,
means the figure reflected across the x-axis then reflected across y-axis.
If a figure reflected across x-axis, then
![(x,y)\to (x,-y)](https://tex.z-dn.net/?f=%28x%2Cy%29%5Cto%20%28x%2C-y%29)
![T(-3,8)\to T_1(-3,-8)](https://tex.z-dn.net/?f=T%28-3%2C8%29%5Cto%20T_1%28-3%2C-8%29)
If a figure reflected across y-axis, then
![(x,y)\to (-x,y)](https://tex.z-dn.net/?f=%28x%2Cy%29%5Cto%20%28-x%2Cy%29)
![T_1(-3,-8)\to T'(-(-3),-8)](https://tex.z-dn.net/?f=T_1%28-3%2C-8%29%5Cto%20T%27%28-%28-3%29%2C-8%29)
![T_1(-3,-8)\to T'(3,-8)](https://tex.z-dn.net/?f=T_1%28-3%2C-8%29%5Cto%20T%27%283%2C-8%29)
Therefore, the required point is T'(3,-8).