\(A=\left(3x\right)^3+\left(2\right)^3\)-(x2-9)
=27x3+8-x2+9
=27x3-x2+17.
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Rút gọn
a) \(\left(\frac{4}{x^3-9x}+\frac{1}{x+3}\right):\left(\frac{x-3}{x^2+3x}-\frac{x}{3x+9}\right)\)
b) \(\left(\frac{2}{x-2}-\frac{2}{x+2}\right).\frac{x^2+4x+4}{8}\)
c) \(\left(\frac{3x}{1-3x}+\frac{2x}{3x+1}\right):\frac{6x^2+10x}{1-6x+9x^2}\)
CMR :\(X^6+27=\left(X^2+3\right)\left(X^4-3X^2+9\right)=\left(X^2+3x+3\right)\left(X^4-3X^3+6X^2-9x+9\right)\)
thực hiện phép tính:
a,\(\left(9x^2y^3-15x^4y^4\right):3x^2y-\left(2-3x^2y\right)y^2\)
b,\(\left(6x^2-xy\right):x+\left(2x^3y+3xy^2\right):xy-\left(2x-1\right)x\)
c,\(\left(x^2-xy\right):x-+\left(6x^2y^5-9x^3y^4+15x^4y^2\right):\dfrac{3}{2}x^2y^3\)
Chứng minh rằng biểu thức sau không phụ thuộc vào biến x:
a/A=\(\left(3x-2\right)\left(9x^2+6x+4\right)-3\left(9x^2-2\right)\)
b/B=\(\left(3x+5\right)^2+\left(6x+10\right)\left(2x-3x\right)+\left(2-3x\right)^2\)
BT6: Thu gọn về hàng đẳng thức
\(3,\left(x+3\right)^2+\left(x-2\right)^2-2\left(x+3\right)\left(x-2\right)\)
\(4,\left(3x-5\right)^2-2\left(3x-5\right)\left(3x+5\right)+\left(3x+5\right)^2\)
Rút gon biểu thức sau
a) \(\left(x-5\right)\left(2x+3\right)+2x\left(1-x\right)\)
b) \(\left(3x-5\right)^2-\left(x+5\right)\left(5-x\right)-\frac{5}{2}\left(-2x\right)^2\)
c) \(\left(3x+2\right)\left(4-6x+9x^2\right)-3x\left(3x-2\right)^2+12\left(-\frac{2}{3}-3x^2\right)\)
Tính.
a) \(\left(2x-1\right)\left(2x-3\right)\left(2x-5\right)\)
b)\(\left(3x-2\right)\left(9x^2+6x+4\right)\left(9x^2-6+4\right)\)
c)\(\left(x+y-z\right)\left(x-y+z\right)+\left(y-z\right)^2\)
rút gọn biểu thức sau bằng cách nhanh nhấtA left(a^2+b^2-c^2right)^2-left(a^2-b^2+c^2right)^2-4a^2b^2B left(3x^3+3x+1right)cdotleft(3x^3-3x+1right)-left(3x^3+1right)^2C left(2-6xright)^2+left(2-5xright)^2+2cdotleft(6x-2right)cdotleft(2-5xright)D 5cdotleft(3x-1right)^2+4cdotleft(5x+1right)^2-12cdotleft(5x-2right)left(5x+2right)E left(3x-1right)^2+left(2x+4right)cdotleft(1-3xright)+left(x+2right)^2G left(x-1right)^3+4cdotleft(x+1right)cdotleft(1-xright)+3cdotleft(x-1right)cdotleft(x^2+x+1rig...
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rút gọn biểu thức sau bằng cách nhanh nhất
A = \(\left(a^2+b^2-c^2\right)^2-\left(a^2-b^2+c^2\right)^2-4a^2b^2\)
B = \(\left(3x^3+3x+1\right)\cdot\left(3x^3-3x+1\right)-\left(3x^3+1\right)^2\)
C = \(\left(2-6x\right)^2+\left(2-5x\right)^2+2\cdot\left(6x-2\right)\cdot\left(2-5x\right)\)
D = \(5\cdot\left(3x-1\right)^2+4\cdot\left(5x+1\right)^2-12\cdot\left(5x-2\right)\left(5x+2\right)\)
E = \(\left(3x-1\right)^2+\left(2x+4\right)\cdot\left(1-3x\right)+\left(x+2\right)^2\)
G = \(\left(x-1\right)^3+4\cdot\left(x+1\right)\cdot\left(1-x\right)+3\cdot\left(x-1\right)\cdot\left(x^2+x+1\right)\)
Thu gọn \(\dfrac{20x^2+120x+180}{\left(3x+5\right)^2-4x^2}+\dfrac{5x^2-125}{9x^2-\left(2x+5\right)^2}-\dfrac{\left(2x+3\right)^2-x^2}{3\left(x^2+8x+15\right)}\)