a: \(=-\left(10x^2+15x-8x-12\right)=-10x^2-7x+12\)

-10x^2-7x+12

\(\dfrac{5x+5y}{3x-3y}:\dfrac{5x}{x^2-y^2}.\)

\(=\dfrac{5\left(x+y\right)}{3\left(x-y\right)}.\dfrac{\left(x-y\right)\left(x+y\right)}{5x}.\)

\(=\dfrac{x+y}{3}.\dfrac{x+y}{x}.\)

\(=\dfrac{\left(x+y\right)^2}{3x}.\)

Cảm ơn nha

1: ĐKXĐ:  \(x\notin\left\{0;3\right\}\)

\(\dfrac{x+3}{x}-\dfrac{x}{x-3}+\dfrac{9}{x^2-3x}\)

\(=\dfrac{x+3}{x}-\dfrac{x}{x-3}+\dfrac{9}{x\left(x-3\right)}\)

\(=\dfrac{\left(x+3\right)\left(x-3\right)-x^2+9}{x\left(x-3\right)}\)

\(=\dfrac{x^2-9-x^2+9}{x\left(x-3\right)}\)

=0

2: ĐKXĐ: \(x\notin\left\{0;1\right\}\)

\(\dfrac{3}{x}-\dfrac{5}{x-1}+\dfrac{3x+2}{x^2-x}\)

\(=\dfrac{3}{x}-\dfrac{5}{x-1}+\dfrac{3x+2}{x\left(x-1\right)}\)

\(=\dfrac{3x-3-5x+3x+2}{x\left(x-1\right)}\)

\(=\dfrac{x-1}{x\left(x-1\right)}=\dfrac{1}{x}\)

\(=1.\left(2+1\right)\left(2^2+1\right)...\left(2^{256}+1\right)=\left(2-1\right)\left(2+1\right)...\left(2^{256}+1\right)\)

\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{256}+1\right)=\left(2^4-1\right)...\left(2^{256}+1\right)=....=2^{512}-1\)

A= (2-1) (2+1) (22+1) ........ + 1
= (22-1)(22+1) ......... (2256+1)
= (24-1) (24+ 1) ......... (2256+1)
................
= [(2256)2 –1] + 1
= 2512

1. 2x²y(2x²+3x+3)

    = 4x⁴y +6x³y+6x²y

2) ( 4x²y + 6xy² - 2x )1/2xy²

   = 2x³y³ +3x²y⁴-x²y²