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(2x - 1)(x2 - 2xy + 3y2) = \(2x^3-4x^2y+6xy^2-x^2+2xy-3y^2\)
a, \(\left(x-2\right)^2+\left(3-x\right)\cdot\left(x-1\right)\)
\(=x^2-4x+4+\left(3x-3-x^2+x\right)\)
\(=x^2-4x+4+3x-3-x^2+x\)
\(=1\)
b, \(\left(x+2\right)^3-x\cdot\left(x^2+6x+12\right)\)
\(=x^3+6x^2+12x+8-x^3-6x^2-12x\)
\(=8\)
a, \(3\left(2x+1\right)^2-2\left(x-5\right)^2+\left(x-1\right)\left(x+2\right)\)
\(=3\left(4x^2+4x+1\right)-2\left(x^2-10x+25\right)+x^2+x-2\)
\(=12x^2+12x+3-2x^2+20x-50+x^2+x-2\)
\(=11x^2+33x-49\)
\(3\left(2x+1\right)^2-2\left(x-5\right)^2+\left(x-1\right)\left(x+2\right)\)
\(=3\left(4x^2+4x+1\right)-2\left(x^2-10x+10\right)+x^2+2x-x-2\)
\(=12x^2+12x+3-2x^2-20x-20+x^2+2x-x-2\)
\(=11x^2+33x-15\)
\(\left(x^2-9\right)^2-\left(x+3\right)\left(x-3\right)\left(x^2+9\right)=\left(x-3\right)^2\left(x+3\right)^2-\left(x+3\right)\left(x-3\right)\left(x^2+9\right)\)
\(=\left(x-3\right)\left(x+3\right)\left[\left(x-3\right)\left(x+3\right)-x^2+9\right]=\left(x-3\right)\left(x+3\right)\left[x^2-9-x^2-9\right]=\left(x-3\right)\left(x+3\right)\cdot\left(-18\right)\)
\(=-18\left(x+3\right)\left(x-3\right)\)
a) 3(x + 1) - 3x = 3x + 3 - 3x = (3x - 3x) + 3 = 3
b) x3 - x(x2 - 2) = x3 - x3 + 2x = (x3 - x3) + 2x = 2x
Bài làm:
a) \(3\left(x+1\right)-3x\)
\(=3x+3-3x\)
\(=3\)
b) \(x^3-x\left(x^2-2\right)\)
\(=x^3-x^3+2x\)
\(=2x\)
a) \(\left(2x^2-3x\right)\left(5x^2-2x+1\right)\)
\(=10x^4-4x^3+2x^2-15x^3+6x^2-3x\)
\(=10x^4-19x^3+8x^2-3x\)
b) \(\left(x+1\right)\left(x^2-x+1\right)-x\left(x+3\right)\left(x+5\right)\)
\(=x^3+1-x\left(x^2+8x+15\right)\)
\(=x^3+1-x^3-8x^2-15x\)
\(=-8x^2-15x+1\)