`(3xy. 4x)(2xy^2 - 6x+4)`

`= 6x^2. y^3 - 18x^2 y+ 12xy-4x (2y^2 - 6x+4)`

`= 6x^2y^3 - 8x^2y^2 - 18x^2y + 12xy + 24x^2 - 16x`

`A=1.2+2.3+3.4+4.5+...+99.100`

`3A= 1.2.3 + 2.3.3 + 3.4.3 + 4.5.3+ … + 99.100.3`
`3A= 1.2.3 + 2.3.(4 - 1) + 3.4.( 5 - 2) + … + 99.100. (101 - 98)`
`3A= 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + … + 99.100.101 - 98.99.100`
`3A = 99.100.101`
`A = (99.100.101)/3`
`A = 333 300`

`(x^2 y + xy^2)(x-y)=xy(x-y)(x+y)`

Ta có VT `=(x^2 y + xy^2)(x-y)`

=> `VT=xy(x+y)(x-y)=xy(x-y)(x+y)=VP` (đpcm) 

Áp dụng bất đẳng thức Cauchy-Schwarz cho `x;y;z` , ta có:

`(\sqrt{a + b} + \sqrt{b + c} + \sqrt{c + a})^2 \leq 3. ((a + b) + (b + c) + (c + a)) = 3.2 = 6`

-> `\sqrt{a + b} + \sqrt{b + c} + \sqrt{c + a} \leq \sqrt{6}` (đpcm)

`(4^21. (-3)^40)/(6^41) = (2^42. 3^40)/(2^41. 3^41)=2/3`

`575- (6x+70)= 445`

`6x+70=130`

`6x=60`

`x= 60/6`

`x=10`

Vậy `x=10`

`ab0-ab=558`

-> `10.ab-ab=558`

-> `ab(10-1)=558`

-> `ab.9=558`

-> `ab= 62`

`ab0-ab=558`

-> `10.ab-ab=558`

-> `ab(10-1)=558`

-> `ab.9=558`

-> `ab= 62`

Tổng của hai số là:

`45678-3285= 42393`

Đáp số: `42393`

`A= 2^1 + 2^2+ 2^3+...+2^39+ 2^40`

`2A= 2^2 + 2^3+ 2^4+...+ 2^40 + 2^41`

`2A-A= (2^2+2^3+2^4+...+2^40 +2^41)-(2^1+2^2+2^3+..+2^39+2^40)`

`A= 2^41-2`