\(\text{(a+b+c)(ab+bc+ca)-abc}=a^2b+ab^2+ac^2+ca^2+bc^2+cb^2+abc+abc+abc-abc\)

\(=ab\left(a+b\right)+c^2\left(a+b\right)+bc\left(a+b\right)+ca\left(a+b\right)=\left(a+b\right)\left(c^2+ab+bc+ca\right)\)

\(=\left(a+b\right)\left[c\left(c+b\right)+a\left(c+b\right)\right]=\left(a+b\right)\left(b+c\right)\left(c+a\right)\)=> đpcm

1²+4²+7²+10²+...+97²+100²

=1+(1+3)4+(4+3)7+(7+3)10+...+(94+3)97+(97+3)100

=1+3.4+1.4+4.7+3.7+7.10+3.10+...+94.97+3.97+97.100+3.100

=1+(3.4+3.7+3.10+...+3.97+3.100+1.4)+(4.7+7.10+...+97.100)

=1+1716+4+(4.7+7.10+...+97.100)

=1721+(4.7+7.10+...+97.100)

đặt A=4.7+7.10+...+97.100

=>9A=4.7.9+7.10.9+...+97.100.9

=4.7(10-1)+7.10(13-4)+...+97.100.(103-94)

=4.7.10-1.4.7+7.10.13-4.7.10+...+97.100.103-94.97.100

=97.100.103-1.4.7=999100-28

=999072

=>A=999072:9=111008

=>1²+4²+7²+10²+...+97²+100²=1721+111008=112729

Điểm M trong hình vẽ dưới biểu diễn số phức z. Khi đó |z| bằng bao nhiêu ?

A. 3.

B.5.

C. 4.

D. 25.

Hello. My name is ... I am .... years old .There are four people in my family. My mom, dad, sister and me. My mom is thirty years old. She is a teacher. My dad is thirty-five years old. He is a doctor .  My sister is ten years old. She is a student . And me I am a student.I love my family
 

101 - 102 + 103 - 104 + 105 - 106 +........ + 997 - 998 + 999 

= 999 - [102-101+104-103+...+998-997] = 999- [1+1+...+1] [449 số 1]

=999 -499 = 500