$A=3+3^2+3^3+\dots+3^{100}$

$3A=3^2+3^3+3^4+\dots+3^{101}$

$3A-A=(3^2+3^3+3^4+\dots+3^{101})-(3+3^2+3^3+\dots+3^{100})$

$2A=3^{101}-3$

$\Rightarrow 2A+3=3^{101}$

Mặt khác: $2A+3=3^n$. Do đó: $3^n=3^{101}\Rightarrow n=101$ (tmdk)

a, Chu vi mảnh ruộng là:

$(20+12)\times2=64$ (m)

Diện tích mảnh ruộng là:

$20\times12=240$ (m²)

b. Số tiền công bác nông dân nhận được là:

$4000\times240=960000$ (đồng)

Anh xem lại ý b nhé.

a) $(x^2-1)(x^2+2x)$

$=x^2(x^2+2x)-(x^2+2x)$

$=x^4+2x^3-x^2-2x$

b) $(x^2-2xy+y^2)(x-y)$

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

$=x^3-2x^2y+xy^2-x^2y+2xy^2-y^3$

$=x^3-3x^2y+3xy^2-y^3$

c) $(x+3)(x^2+3x-5)$

$=x(x^2+3x-5)+3(x^2+3x-5)$

$=x^3+3x^2-5x+3x^2+9x-15$

$=x^3+6x^2+4x-15$

a) $3x(2x^2+x-1)$

$=3x.2x^2+3x.x+3x.(-1)$

$=6x^3+3x^2-3x$

b) $-2x(x^2-5x-1)$

$=-2x.x^2-2x.(-5x)-2x.(-1)$

$=-2x^3+10x^2+2x$

c) $(x+1)(x^2-x+1)$

$=x(x^2-x+1)+(x^2-x+1)$

$=x^3-x^2+x+x^2-x+1$

$=x^3+1$

d) $(5x+2)(2x^3-3x-1)$

$=5x(2x^3-3x-1)+2(2x^3-3x-1)$

$=10x^4-15x^2-5x+4x^3-6x-2$

$=10x^4+4x^3-15x^2-5x-2$

\(\left(x^2-1\right)+\left(y^2-1\right)+2x^2y^2\\ =\left(x^2+y^2\right)-2+2x^2y^2\\ =2-2+2x^2y^2=2x^2y^2\)

\(\left(x^2-9\right)-9\left(x-3\right)^2=0\\ \Leftrightarrow\left(x-3\right)\left(x+3\right)-9\left(x-3\right)^2=0\\ \Leftrightarrow\left(x-3\right)\left[\left(x+3\right)-9\left(x-3\right)\right]=0\\ \Leftrightarrow\left(x-3\right)\left(x+3-9x+27\right)=0\\ \Leftrightarrow\left(x-3\right)\left(30-8x\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x-3=0\\30-8x=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=3\\x=\dfrac{15}{4}\end{matrix}\right.\)