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1)
a. \(\left(3x^2-50\right)^2=5^4\)
\(\Leftrightarrow3x^4-50=625\)
\(\Leftrightarrow3x^4=675\)
\(\Leftrightarrow x^4=225\)
\(\Leftrightarrow x=\sqrt{15}\)
2)
a. \(\frac{\left(3^4-3^3\right)^4}{27^3}=\frac{3^{16}-3^{12}}{\left(3^3\right)^3}=\frac{3^{12}.3^4-3^{12}}{3^9}=\frac{3^{12}\left(3^4-1\right)}{3^9}\)
\(=\frac{3^{12}.80}{3^9}=3^3.80=27.80=2160\)
b. \(\frac{25^3}{\left(5^5-5^3\right)^2}=\frac{\left(5^2\right)^3}{5^{10}-5^6}=\frac{5^6}{5^6.5^4-5^6}=\frac{5^6}{5^6\left(5^4-1\right)}\)
\(=\frac{5^6}{5^6.624}=\frac{1}{624}\)
\(a,-3x^2+7x-9+\left(x-1\right)\left(x+2\right)\\ =-3x^2+7x-9+x^2-x+2x-2\\ =\left(-3x^2+x^2\right)+\left(7x-x+2x\right)-\left(9+2\right)\\ =-2x^2+8x-11\\ b,x\left(x-5\right)-2x\left(x+1\right)\\ =x^2-5x-2x^2-2x\\ =\left(x^2-2x^2\right)-\left(5x+2x\right)\\ =-3x^2-7x\\ c,4x\left(x^2-x+1\right)-\left(x-1\right)\left(x^2-x\right)\\ =4x^3-4x^2+4x-x\left(x^2-x\right)+x^2-x\\ =4x^3-4x^2+4x-x^3+x^2+x^2-x\\ =\left(4x^3-x^3\right)+\left(-4x^2+x^2+x^2\right)+\left(4x-x\right)\\ =3x^3-2x^2+3x\\ =x\left(3x^2-2x+3\right)\)
\(d,-5x\left(x-5\right)+\left(x-3\right)\left(x^2-7\right)\\ =-5x^2+25x+x\left(x^2-7\right)-3\left(x^2-7\right)\\ =-5x^2+25x+x^3-7x-3x^2+21\\ =\left(-5x^2-3x^2\right)+\left(25x-7x\right)+x^3+21\\ =-8x^2+x^3+18x+21\)
1) \(\left(x+2\right)^3-\left(x+6\right)^2-\left(x+1\right)\left(x^2-x+1\right)\)
\(=x^3+3.x^2.2+3.x.2^2+2^3-\left(x^2+2.x.6+6^2\right)-\left(x^3+1\right)\)
\(=x^3+6x^2+12x+8-x^2-12x-36-x^3-1\)
\(=5x^2-29\)
2. \(\left(x-3\right)\left(x^2+3x+9\right)-\left(x+3\right)^2\)
\(=x^3-3^3-\left(x^2+2.x.3+3^2\right)\)
\(=x^3-27-x^2-6x-9\)
\(=x^3-x^2-6x-36\)
\(=x^3-2x^2+3x^2-6x-36\)
\(=x^2\left(x-2\right)+3x\left(x-2\right)-36\)
\(=x\left(x-2\right)\left(x+3\right)-36\)
3. \(\left(2x-1\right)^2+2x^2.\left(x-2\right)\left(x+3\right)^2\)
\(=4x^2-4x+1+2x^2\left(x-2\right)\left(x^2+6x+9\right)\)
\(=4x^2-4x+1+2x^2\left(x^3+6x^2+9x-2x^2-12x-18\right)\)
\(=4x^2-4x+1+2x^2\left(x^3+4x^2-3x-18\right)\)
\(=4x^2-4x+1+2x^5+8x^4-6x^3-36x^2\)
\(=2x^5+8x^4-6x^3-32x^2-4x+1\)
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P/s: Không chắc lắm