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\(A=x^5+2x^4+4x^3+8x^2+16x-2x^4-4x^3-8x^2-16x-32\)
\(=x^5-32\)(1)
Thay x=3 vào (1) ta được:
\(A=3^5-32=243-32=211\)
\(\left(x-2\right)\left(x^2-2x+1\right)\left(x+2\right)\left(x^2+2x+4\right)\)
\(=\left[\left(x-2\right)\left(x^2+2x+4\right)\right]\left[\left(x+2\right)\left(x^2-2x+4\right)\right]\)
\(=\left(x^3-8\right)\left(x^3+8\right)\)
\(=x^6-64\)
\(\left(x-2\right)\left(x^2-2x+4\right)\left(x+2\right)\left(x^2+2x+4\right)\)
\(=\left(x-2\right)\left(x^2+2x+4\right)\left(x+2\right)\left(x^2-2x+4\right)\)
\(=\left(x^3-8\right)\left(x^3+8\right)\)
\(=x^6+64\)
\(\frac{4}{x+2}+\frac{3}{x-2}+\frac{-5x-2}{x^2-4}\)ĐK : \(x\ne\pm2\)
\(=\frac{4\left(x-2\right)+3\left(x+2\right)-5x-2}{\left(x+2\right)\left(x-2\right)}=\frac{4x-8+3x+6-5x-2}{\left(x+2\right)\left(x-2\right)}\)
\(=\frac{2x-4}{\left(x+2\right)\left(x-2\right)}=\frac{2\left(x-2\right)}{\left(x+2\right)\left(x-2\right)}=\frac{2}{x+2}\)
\(\left(\frac{4}{x-4}-\frac{4}{x+4}\right)\times\frac{x^2+8x+16}{32}\)
ĐKXĐ : \(x\ne\pm4\)
\(=\left(\frac{4\left(x+4\right)}{\left(x-4\right)\left(x+4\right)}-\frac{4\left(x-4\right)}{\left(x-4\right)\left(x+4\right)}\right)\times\frac{\left(x+4\right)^2}{32}\)
\(=\left(\frac{4x+16-4x+16}{\left(x-4\right)\left(x+4\right)}\right)\times\frac{\left(x+4\right)^2}{32}\)
\(=\frac{32}{\left(x-4\right)\left(x+4\right)}\times\frac{\left(x+4\right)^2}{32}\)
\(=\frac{x+4}{x-4}\)
\(\left(\frac{4}{x-4}-\frac{4}{x+4}\right).\frac{x^2+8x+16}{32}\)
\(=\left(\frac{4\left(x+4\right)}{\left(x-4\right)\left(x+4\right)}-\frac{4\left(x-4\right)}{\left(x+4\right)\left(x-4\right)}\right).\frac{\left(x+4\right)^2}{32}\)
\(=\frac{4x+16-4x+16}{\left(x-4\right)\left(x+4\right)}.\frac{\left(x+4\right)^2}{32}=\frac{32}{\left(x-4\right)\left(x+4\right)}.\frac{\left(x+4\right)^2}{32}=\frac{x+4}{x-4}\)