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a) (x+2)(x−2)−(x−3)(x+1)
=x2−22−(x2+x−3x−3)
=x2−4−x2−x+3x+3
=2x−12x−1
b) (2x+1)2+(3x−1)2+2(2x+1)(3x−1)(
=(2x+1)2+2.(2x+1)(3x−1)+(3x−1)2
=[(2x+1)+(3x−1)]2
= (2x+1+3x−1)2
=(5x)2=25x2
\(2x\left(2x-1\right)^2-3x\left(x+3\right)\left(x-3\right)-4x\left(x+1\right)^2\)
\(=x\left[2\left(2x-1\right)^2-3\left(x^2-9\right)-4\left(x+1\right)^2\right]\)
\(=x\left(8x^2-8x+1-3x^2+27-4x^2-8x-4\right)\)
\(=x\left(x^2-16x+28\right)=x\left(x-2\right)\left(x-14\right)\)
a)\(x\left(2x^2-3\right)-x^2\left(5x+1\right)+x^2\)
=\(2x^3-3x-5x^3-x^2+x^2=-3x^3-3x\)
b) \(3x\left(x-2\right)-5x\left(1-x\right)-8\left(x^2-3\right)\)
\(=3x^2-6x-5x+5x^2-8x^2+24=-11x+24\)
c) \(\dfrac{1}{2}x^2\left(6x-3\right)-x\left(x^2+\dfrac{1}{2}\right)+\dfrac{1}{2}\left(x+4\right)\)
\(=3x^3-\dfrac{3}{2}x^2-x^3-\dfrac{1}{2}x+\dfrac{1}{2}x+2=2x^3-\dfrac{3}{2}x^2+2\)
a) \(\left(1+x\right)^2+\left(1-x\right)^2\)
\(=1+2x+x^2+1-2x+x^2\)
\(=2x^2+2\)
b) \(\left(x+2\right)^2+\left(1+x\right)\left(1-x\right)\)
\(=x^2+4x+4+1-x^2\)
\(=4x+5\)
c) \(\left(x-3\right)^2+3\left(x+1\right)^2\)
\(=x^2-6x+9+3x^2+6x+3\)
\(=4x^2+12\)
d)\(\left(2+3x\right)\left(3x-2\right)-\left(3x+1\right)^2\)
\(=9x^2-4-9x^2-6x-1\)
\(=-6x-5\)
e) \(\left(x+5\right)\left(x-2\right)-\left(x+2\right)^2\)
\(=x^2-2x+5x-10-x^2-4x-4\)
\(=-x-14\)
f) \(\left(x+3\right)\left(2x-5\right)-2\left(1+x\right)^2\)
\(=2x^2-5x+6x-15-2-4x-2x^2\)
\(=-3x-17\)
g) \(\left(4x-1\right)\left(4x+1\right)-4\left(1-2x\right)^2\)
\(=16x^2-1-4+16x-16x^2\)
\(=16x-5\)
#Học tốt!
\(\left(x^2-1\right)\left(x+2\right)-\left(x-4\right)\left(x^2+4x+16\right)\)
\(=x^3+2x^2-x-2-\left(x^3-4^3\right)\)
\(=x^3+2x^2-x-2-x^3+64\)
\(=2x^2-x+62\)
\(2x\left(3x-2\right)^2\)
\(=2x\left(9x^2-12x+4\right)\)
\(=18x^3-24x^2+8x\)
\(\left(x-3\right)\left(x^2-3x+9\right)\)
\(=x^3-3x^2+9x-3x^2+9x-27\)
\(=x^3-3x^2+18x-27\)
\(\left(x^2-1\right)\left(x+2\right)-\left(x-4\right)\left(x^2+4x+16\right)\)
\(=\left(x^2-1^2\right)\left(x+2\right)-x^3-4^3\)
\(=\left(x+1\right)\left(x-1\right)\left(x+2\right)-x^3-64\)
\(\left(x+1\right)^3+\left(x-1\right)^3+x^3-3x\left(x+1\right)\left(x-1\right)\)
\(=x^3+3x^2+3x+1+x^3-3x^2+3x-1+x^3-3x\left(x^2-1\right)\)
\(=3x^3+6x-3x^4+3x\)
\(=-3x^4+3x^3+9x\)
\(x^3+3x^2y+3xy^2+y^3\) \(+x^3-3x^2y+3xy^2-y^3\)\(+x^3-3x\left(x^2-1\right)\)
\(=3x^3+6xy^2-3x^3+3x\)
\(=3x\left(1+2y^2\right)\)