a. Ta có:

\(\left\{{}\begin{matrix}ME=\dfrac{1}{2}MN\\FQ=\dfrac{1}{2}PQ\\MN=PQ\end{matrix}\right.\) \(\Rightarrow ME=FQ\)

Mặt khác: \(MN//PQ\Rightarrow ME//FQ\)

Tức giác MEFQ có một cặp cạnh đối ME,FQ song song và bằng nhau. Do đó từ giác MEFQ là hình bình hành.

b.Xét tứ giác QENF ta có:

\(EN=\dfrac{1}{2}MN=\dfrac{1}{2}PQ=FQ\)

\(MN//PQ\Rightarrow EN//FQ\)

Tứ giác QENF có cặp cạnh đối EN, FQ song song và bằng nhau nên từ giác QENF là hình bình hành. Suy ra QE = NF.

A= n³-25n=n.(n-5).(n+5)

+ Nếu n lẻ thì (n - 5) chẵn, (n+5) chẵn nên A là số chẵn sẽ chia hết cho 2.

+ Nếu n chẵn thì A chẵn nên A chia hết cho 2

A là tích của 3 số: n ; (n+5) và (n - 5)

+ Nếu n chia hết cho 3 thì A chia hết cho 3

+ Nếu n chia 3 dư 1 thì n+5 chia hết cho 3

+ Nếu n chia 3 dư 2 thì n - 5 chia hết cho 3

Vậy A luôn chia hết cho 2 và 3. Hay A luôn chia hết cho 6

B = n²⁰²⁰.(n²-1) = n²⁰²⁰.(n-1).(n+1)

Chứng minh tương tự câu a

$+,$ Gọi $O$ giao điểm của $AC$ và $BD,$ do $ABCD$ là hình bình hành nên $O$ là trung điểm của $AC$ và $BD.$

Xét $\Delta ADC$ có $DO;AM$ là đường trung tuyến 

$DO\cap AM=G$

$\Rightarrow G$ là trọng tâm $\Delta ADC$

$\Rightarrow AG=$2/3  $AM=$ 2/3 $\times 3GM=2GM$ ( đpcm)

$+,$ $DG=\; 2/3$ $DO=$ 2/3$\times \; 1/2$ $BD$ $=\; 1/3$ $BD$

$\Rightarrow BD=3DG$ ( đpcm)

My home village is now different from the village in my father’s story. In his story, my village is very poor. Everyone live a hard life that time. People lack of food, of money. Now, it is different. People don’t live a hard life anymore. They have enough food, enough money, everyone got a house, and many more things. The only things that doesn’t change is sentiment. Everyone always be very happy. They live together, help each other when they need, that is a luxury. That makes my village a wonderful place for everyone. People are just farmer, but they solidarity in the face of penury. And when they have money in their hands, they still solidarity they are friendly with others, they are helpful, they are good people. Landscape is still like the old days. That river, that mountain. Nature is harmony with people. People live with nature, people product things of nature, and nature always open-handed with people, give them resource for them to build their house. That is what people seek, and they live with it very well. That’s all I can say about my home village, in my opinion, my village is a wonderful place. War does not determine who is right, only who is left:” Ask not what your country can do for you but what you can do for your country”.

-.-

Tick mik

từ câu 13 đến câu 18 của em đây nhé:

13 , 25a² -  49b⁴ = (5a-7b²)(5a+7b²) 

14,100a² - 9b⁴ = (10a -3b²)(10a+3b²)

15, (a⁴  -  4b²) = (a² - 2b)(a²+2b) 

16,\(\dfrac{1}{4}\)a² - b² = (\(\dfrac{1}{2}\) a - b)(\(\dfrac{1}{2}\)a + b)

17, \(\dfrac{1}{4}\)a² - \(\dfrac{1}{9}\)b² = (\(\dfrac{1}{2}\)a- \(\dfrac{1}{3}\)b)(\(\dfrac{1}{3}\)a+ \(\dfrac{1}{3}\)b)

18, \(\dfrac{4}{9}\)a⁴ - \(\dfrac{25}{4}\) = ( \(\dfrac{2}{3}\)a² - \(\dfrac{5}{2}\))( \(\dfrac{2}{3}\)a² + \(\dfrac{5}{2}\))

gõ đoạn tiếng việt rồi cop hết lại dịch sang tiếng anh.

2(3x−1).(2x−1).(4x+1)=.          (12x^2-6x-4x^2+2)(4x+1)=

48x^3+12x^2-24x^2-6x-16x^3-4x^2+8x+2

-16x^2

-16