a) \(153^2-53^2=\left(153-53\right)\left(153+53\right)=100.206=20600\)

b)

\(\left(2020^2-2019^2\right)+\left(2018^2-2017^2\right)+...+\left(2^2-1^2\right)\\ =\left(2020+2019\right)\left(2020-2019\right)+\left(2018+2017\right)\left(2018-2017\right)+...+\left(2+1\right)\left(2-1\right)\\ =2020+2019+2018+2017+...+2+1\\ =\dfrac{\left(2020+1\right)2020}{2}=2041210\)

Lời giải:

a. $153^2-53^2=(153-53)(153+53)=100.206=20600$

b. 

$2020^2-2019^2+2018^2-2017^2+...+2^2-1^2$

$=(2020^2-2019^2)+(2018^2-2017^2)+...+(2^2-1^2)$

$=(2020-2019)(2020+2019)+(2018-2017)(2018+2017)+...+(2-1)(2+1)$

$=2020+2019+2018+2017+...+2+1$

$=\frac{2020.2021}{2}=2041210$

a) 153²-53²=(153-53)(153+53)=100.206=20600

a: =17-70-163+246

=-43-163+246

=246-206

=40

\(\sqrt{2021^2+2022^2+2021^2.2022^2}\)

\(=\sqrt{2021^2+\left(2021+1\right)^2+\left(2021.2022\right)^2}\)

\(=\sqrt{2021^2+2021^2+2.2021+1+\left(2021.2022\right)^2}\)

\(=\sqrt{2.2021.2022+1+\left(2021.2022\right)^2}\)

\(=\sqrt{\left(2021.2022+1\right)^2}\)

\(=2021.2022+1\) là 1 số nguyên (đpcm)

x0x0x : X x 3 – 20202

= 10101 x 3 – 20202

= 30303 – 20202

= 10101

B

B

B

a) 544544 – 444444 = 544.1001 – 444.1001 = 1001.(544 – 444) = 1001.100 = 100100

b) 131313 – 10101 – 20202 = 10101.13 – 10101 – 10101.2

= 10101.(13 – 1 – 2) = 10101.10 = 101010

\(131313-10101-20202=13\cdot10101-10101-2\cdot10101=10101\left(13-1-2\right)=10101\cdot10=101010\)

Bài 1: 

$-1+2-3+4-5+6-7+8-...-2019+2020-2021$

$=(2+4+6+8+...+2020)-(1+3+5+...+2021)$

$=(\frac{2020-2}{2}+1).\frac{2020+2}{2}-(\frac{2021-1}{2}+1).\frac{2021+1}{2}=1021110- 1022121=-1011$

Bài 1 cách 2:

$A=-1+2-3+4-5+6-7+8-....-2019+2020-2021$

$=-1+(2-3)+(4-5)+(6-7)+....+(2020-2021)$

$=-1+\underbrace{(-1)+(-1)+...+(-1)}_{1010}=-1+(-1).1010=-1011$

Bài 2:

$A=10^{2021}+8=(2.5)^{2021}+8=2^{2021}.5^{2021}+8$

$=2^3.2^{2018}.5^{2021}+8=8.2^{2018}.5^{2021}+8$

$=8(2^{2018}.5^{2021}+1)\vdots 8(*)$

Mặt khác:

Gọi $\text{B(9)}$ là bội số của $9$

$A=(9+1)^{2021}+8=\text{B(9)}+1+8=\text{B(9)}+9=\text{B(9)}$

$\Rightarrow A\vdots 9(**)$

Từ $(*); (**)$ mà $9,8$ nguyên tố cùng nhau nên $A\vdots (9.8)$ hay $A\vdots 72$