1. \(125x^3-1=\left(5x\right)^3-1^3=\left(5x-1\right)\left(25x^2+5x+1\right)\)

2. \(8x^3+125=\left(2x\right)^3+5^3=\left(2x+5\right)\left(4x^2-10x+25\right)\)

3. \(x^3+\frac{y^3}{8}=x^3+\left(\frac{y}{2}\right)^3=\left(x+\frac{y}{2}\right)\left(x^2-\frac{xy}{2}+\frac{y^2}{4}\right)\)

5 . chu vi hình thang là 4x7=28 (ABG)

6.(25+10) x24:2 = 79 

7 a hình thang

b . chu vi tứ giác là 15x9=135 

tui nè

\(3\left(x-3\right)+2\left(x-1\right)=3\)

\(\Leftrightarrow3x-9+2x-2=3\)

\(\Leftrightarrow5x=14\)

\(\Leftrightarrow x=\frac{14}{5}\)

Vậy :.......

#H

\(\frac{1}{25}-x^2\)

\(=\left(\frac{1}{5}\right)^2-x^2\)

\(=\left(\frac{1}{5}-x\right)\left(\frac{1}{5}+x\right)\)

#H

x=565>2 nhé

Đáp án C 

\(\frac{CD}{BD}=\frac{AC}{AB}=\frac{3}{4}\)(định lí)

\(\Rightarrow C\)

\(1^2-2^2+3^2-4^2+...+2009^2-2010^2+2011^2\)

\(=1^2+\left(3^2-2^2\right)+\left(5^2-4^2\right)+...+\left(2011^2-2010^2\right)\)

\(=1+\left(3-2\right)\left(3+2\right)+\left(5-4\right)\left(5+4\right)+...+\left(2011-2010\right)\left(2011+2010\right)\)

\(=1+2+3+...+2010+2011\)

\(=\frac{2011.2012}{2}=2023066\)

a) \(-5x^2-2xy-2y^2+14x-10y-1\)

\(=-x^2-y^2-9-2xy+6x+6y-4x^2+8x-4-y^2+4y-4+16\)

\(=-\left(x+y-3\right)^2-4\left(x-1\right)^2-\left(y-2\right)^2+16\le16\)

Dấu \(=\)khi \(\hept{\begin{cases}x+y-3=0\\x-1=0\\y-2=0\end{cases}}\Leftrightarrow\hept{\begin{cases}x=1\\y=2\end{cases}}\).

b) \(-8x^2-3y^2-26x+6y+100\)

\(=-8\left(x+\frac{13}{8}\right)^2-3\left(y-1\right)^2+\frac{993}{8}\le\frac{993}{8}\)

Dấu \(=\)khi \(\hept{\begin{cases}x+\frac{13}{8}=0\\y-1=0\end{cases}}\Leftrightarrow\hept{\begin{cases}x=-\frac{13}{8}\\y=1\end{cases}}\)