\(B=\dfrac{2^{10}\cdot3^8-2^{10}\cdot3^{10}}{2^{10}\cdot3^8+2^{10}\cdot3^8\cdot5}=\dfrac{2^{10}\cdot3^8\left(1-3^2\right)}{2^{10}\cdot3^8\left(1+5\right)}=\dfrac{1-9}{6}=\dfrac{-8}{6}=-\dfrac{4}{3}\)

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\(1-\)\(a,\frac{7}{8}-\frac{2}{3}=\frac{21}{24}-\frac{16}{24}=\frac{5}{24}\)

\(b,\frac{7}{8}-\frac{2}{3}\times\frac{3}{4}=\frac{7}{8}-\frac{1}{2}=\frac{7}{8}-\frac{4}{8}=\frac{3}{8}\)

\(2-\)\(a,\frac{5}{8}-x=\frac{5}{9}\)

\(x=\frac{5}{8}-\frac{5}{9}\)

\(x=\frac{5}{72}\)

\(b,\frac{3}{4}:x=\frac{2}{5}\)

\(x=\frac{3}{4}:\frac{2}{5}\)

\(x=\frac{15}{8}\)

1, Tính:

\(\frac{7}{8}\) - \(\frac{2}{3}\) = \(\frac{21}{24}\) - \(\frac{16}{24}\) = \(\frac{5}{24}\)

\(\frac{7}{8}\) - \(\frac{2}{3}\) x \(\frac{3}{4}\) = \(\frac{7}{8}\) - \(\frac{1}{2}\) = \(\frac{7}{8}\) - \(\frac{4}{8}\) = \(\frac{3}{8}\)

2, Tìm x

\(\frac{5}{8}\)- x = \(\frac{5}{9}\)

           x = \(\frac{5}{8}\)- \(\frac{5}{9}\)

           x = \(\frac{5}{72}\)

\(\frac{3}{4}\): x = \(\frac{2}{5}\)

           x = \(\frac{3}{4}\) : \(\frac{2}{5}\)

           x = \(\frac{15}{8}\)

\(\Rightarrow\left(x-1\right)^2-\left(2x-3\right)^2=0\\ \Rightarrow\left(x-1-2x+3\right)\left(x-1+2x-3\right)=0\\ \Rightarrow\left(2-x\right)\left(3x-4\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=2\\x=\dfrac{4}{3}\end{matrix}\right.\)

Nguyễn Hoàng Minh  thank you

\(\left\{{}\begin{matrix}4x^2-12x+9\\x^2+10x+25\end{matrix}\right.\)

=2x² - 2.2x.3 + 3²

=4x²-12x+ 9

b) =x²+ 2.x.5+5²

=x²+ 10x+25

a)\(x^8+x^4+1\)

\(=\left(x^8+2x^4+1\right)-x^4\)

\(=\left(x^4+1\right)^2-x^4\)

\(=\left(x^4-x^2+1\right)\left(x^4+x^2+1\right)\)

\(=\left(x^4-x^2+1\right)\left(x^2-x+1\right)\left(x^2+x+1\right)\)

b)\(x^{10}+x^5+1\)

\(=\left(x^{10}+x^9+x^8\right)-\left(x^9+x^8+x^7\right)+\left(x^7+x^6+x^5\right)-\left(x^6+x^5+x^4\right)+\left(x^5+x^4+x^3\right)-\left(x^3+x^2+x\right)+\left(x^2+x+1\right)\)

\(=x^8\left(x^2+x+1\right)-x^7\left(x^2+x+1\right)+x^5\left(x^2+x+1\right)-x^4\left(x^2+x+1\right)+x^3\left(x^2+x+1\right)-x\left(x^2+x+1\right)+\left(x^2+x+1\right)\)

\(=\left(x^2+x+1\right)\left(x^8-x^7+x^5-x^4+x^3-x+1\right)\)

a) \(x^8+x^4+1\)

= \(x^8+2x^4-x^4+1\)

= \(\left(x^4+1\right)^2-x^4\)

= \(\left(x^4-x^2+1\right)\left(x^4+x^2+1\right)\)

= \(\left(x^4-x^2+1\right)\left(x^4+2x^2-x^2+1\right)\)

= \(\left(x^4-x^2+1\right)\left[\left(x^2+1\right)^2-x^2\right]\)

= \(\left(x^4-x^2+1\right)\left(x^2+1-x^2\right)\left(x^2+1+x^2\right)\)

= \(\left(x^4-x^2+1\right)\left(2x^2+1\right)\)

b) \(x^{10}+x^5+1\)

= ( x¹⁰+x⁹+x⁸) - (x⁹+x⁸+x⁷) + (x⁷+x⁶+x⁵) - (x⁶+x⁵+x⁴) + (x⁵+x⁴+x³) - (x³+x²+x) + (x²+x+1)

= (x²+x+1)(x⁸ - x⁷+x⁵-x⁴+x³-x+1)