\(\dfrac{2.6^9-2^5.18^4}{2^2.6^8}\\ =\dfrac{2.\left(2.3\right)^9-2^5.\left(2.3^2\right)^4}{2^2.\left(2.3\right)^8}\\ =\dfrac{2.2^9.3^9-2^5.2^4.\left(3^2\right)^4}{2^2.2^8.3^8}\\ =\dfrac{2.2^9.3^9-2^5.2^4.3^8}{2^{10}.3^8}\\ =\dfrac{2^{10}.3^9-2^9.3^8}{2^{10}.3^8}\\ =\dfrac{2^9.3^8\left(2.3-1\right)}{2^{10}.3^8}\\ =\dfrac{6-1}{2}\\ =\dfrac{5}{2}\)

Nửa chu vi thửa ruộng là:

`100:2=50(m)`

Chiều dài thửa ruộng là:

`50:(2+3)xx3=30(m)`

Chiều rộng thửa ruộng là:

`50-30=20(m)`

Diện tích thửa ruộng là:

`30xx20=600(m^2)`

Thu hoạc được số kg thóc là:

`600:100xx60=360(kg)`

Đáp số: `360kg`

`-2` không phải `+2` nhé :)

`B=(5x-9)^2 + 2(5x-9)(5x+9)+(5x+9)^2`

`=[(5x-9) +(5x+9)]^2`

`=(5x-9+5x+9)^2`

`=(10x)^2`

`=100x^2`

Thay `x=1/10` vào `B` ta có:

`B= 100x^2 = 100 . (1/10)^2 = 100 . 1/100 = 1`

\(\dfrac{x}{x-4}+\dfrac{1}{\sqrt{x}-2}+\dfrac{1}{\sqrt{x}+2}\\ =\dfrac{x}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}+\dfrac{\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}+\dfrac{\sqrt{x}-2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\\ =\dfrac{x+\sqrt{x}+2+\sqrt{x}-2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\\ =\dfrac{x+2\sqrt{x}}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\\ =\dfrac{\sqrt{x}\left(\sqrt{x}+2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\\ =\dfrac{\sqrt{x}}{\sqrt{x}-2}\)

`(x^3 +x^2 -x+a) vdots (x+2)`

`=>(x^3 +2x^2 -x^2 -2x+x+2-2+a) vdots (x+2)`

`=>[x^2 (x+2) - x(x+2)+(x+2)+(a-2)] vdots (x+2)`

`=>[(x^2 -x+1)(x+2) +(a-2)] vdots (x+2)`

Vì `(x^2 -x+1)(x+2) vdots x+2` `=> a-2=0=>a=2`

`x^3 +2x^2 y +xy^2 -4x`

`=x(x^2 +2xy+y^2 -4)`

`=x[(x+y)^2 -2^2]`

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

`(7x+1)^2 -(x-5)^2`

`=[(7x+1)-(x-5)][(7x+1)+(x-5)]`

`=(7x+1-x+5)(7x+1+x-5)`

`=(6x+6)(8x-4)`

`=6(x+1).4(2x-1)`

`=24(x+1)(2x-1)`

`x^4 -6x^3 +54x-81`

`=x^4 -6x^3 +9x^2 -9x^2 +54x-81`

`=(x^4 -6x^3 +9x^2)-(9x^2 -54x+81)`

`=x^2 (x^2 -6x+9)-9(x^2 -6x+9)`

`=(x^2 -6x+9)(x^2 -9)`

`=(x-3)^2 .(x-3)(x+3)`

`=(x+3)(x-3)^3` 

`(x+2)(x+3)(x+4)(x+5)-8`

`=[(x+2)(x+5)][(x+3)(x+4)]-8`

`=(x^2 +7x+10)(x^2 +7x+12)-8`

`=(x^2 +7x+10)^2 +2(x^2 +7x+10)-8`

`=(x^2 +7x+10)^2 +4(x^2 +7x+10)-2(x^2 +7x+10)-8`

`=(x^2 +7x+10)(x^2 +7x+10+4)-2(x^2 +7x+10+4)`

`=(x^2 +7x+10-2)(x^2 +7x+10+4)`

`=(x^2 +7x+8)(x^2 +7x+14)`