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\(\left(x+y+z\right)^3-x^3-y^3-z^3.\)
\(=x^3+y^3+z^3+3\left(x+y\right)\left(x+z\right)\left(y+z\right)-x^3-y^3-z^3\)
\(=3\left(x+y\right)\left(x+z\right)\left(y+z\right)\)
~ Chúc bạn học tốt~
\(x^2\) - \(x\) - 121
= (\(x^2\) - \(2.x.\frac{1}{2}\) + \(\frac{1}{4}\) ) - \(\frac{1}{4}\) - 121
= (\(x\) - \(\frac{1}{2}\) )2 - \(\frac{485}{4}\)
= (\(x\) - \(\frac{1}{2}\) - \(\frac{\sqrt{485}}{2}\) ) (\(x\) - \(\frac{1}{2}\) + \(\frac{\sqrt{485}}{2}\) )
= (\(x\) - \(\frac{1+\sqrt{485}}{2}\) ) (\(x\) - \(\frac{1-\sqrt{485}}{2}\) )
\(x^2-x-121\)
\(=\left(x^2-2.x.\frac{1}{2}+\frac{1}{4}\right)-\frac{1}{4}-121\)
\(=\left(x-\frac{1}{2}\right)^2-\frac{485}{4}\)
\(=\left(x-\frac{1}{2}-\frac{\sqrt{485}}{2}\right)\left(x-\frac{1}{2}+\frac{\sqrt{485}}{2}\right)\)
\(=\left(x-\frac{1+\sqrt{485}}{2}\right)\left(x-\frac{1-\sqrt{485}}{2}\right)\)
a) Ta có : (x - 5)2 - 16
= (x - 5)2 - 42
= (x - 5 - 4)(x - 5 + 4)
= (x - 1)(x - 9)
b) 25 - (3 - x)2
= 52 - (3 - x)2
= (5 - 3 + x)(5 + 3 - x)
= (x + 2)(8 - x)
c) (7x - 4)2 - (2x + 1)2
= (7x - 4 - 2x - 1)(7x - 4 + 2x + 1)
= (5x - 5)(9x - 3)
= 5(x - 1)3(3x - 1)
= 15(x - 1)(3x - 1)
\(x^3-x^2-21x+45\)
\(=\left(x^3-3x^2\right)+\left(2x^2-6x\right)+\left(-15x+45\right)\)
\(=x^2\left(x-3\right)+2x\left(x-3\right)-15\left(x-3\right)\)
\(=\left(x^2+2x-15\right)\left(x-3\right)\)
\(=\left[\left(x^2-3x\right)+\left(5x-15\right)\right]\left(x-3\right)\)
\(=\left[x\left(x-3\right)+5\left(x-3\right)\right]\left(x-3\right)\)
\(=\left(x+5\right)\left(x-3\right)^2\)
\(2x^2+3x-27\)
\(=2x^2+9x-6x-27\)
\(=x\left(2x+9\right)-3\left(2x+9\right)\)
\(=\left(2x+9\right)\left(x-3\right)\)
2x2=>la nhan tuc2x2
3xla tam tu3x
2x2+3x-27=nhan tu pi35x2