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a)\(9x^2+30x+25+9x^2-30x+25-\left(9x^2-2^2\right)\)
=\(9x^2+54\)=\(9\left(x^2+6\right)\)
b)\(2x\left(4x^2-4x+1\right)-3x\left(x^2-9\right)-4x\left(x^2+2x+1\right)\)
=\(8x^3-8x^2+2x-3x^3+27x-4x^3-8x^2-4x\)
=\(x^3-16x^2+25x\)
c)\(\left(x+y-z\right)^2-2\left(x+y-z\right)\left(x+y\right)+\left(x+y\right)^2\)
=\(\left(x+y-z-\left(x+y\right)\right)^2\)=\(\left(-z\right)^2\)
1: \(=x^3-6x^2+12x-8-8x^3-36x^2-54x-27+7\left(x-1\right)^3\)
\(=-7x^3-42x^2-42x-35+7x^3-21x^2+21x-7\)
\(=-63x^2-21x-42\)
2: \(=x^3+125-\left(x^3-8\right)=125+8=133\)
3: \(=8x^3-27-8x^3-12x^2-6x-1=-12x^2-6x-28\)
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!
B = (x-1)(2x+1) - (x2-2x-1)
B = 2x2+x-2x-1-x2-2x-1 = x2-3x-2
B = x2+x-4x-2 = x(x+1) - 4(x+1)
B = (x+1)(x-4)
\(A=2x\left(x-2\right)-x\left(2x-3\right)\\ =2x^2-4x-2x^2+3x\\ =-x\\ B=\left(x-1\right)\left(2x+1\right)-\left(x^2-2x-1\right)\\ =x\left(2x+1\right)-\left(2x+1\right)-x^2+2x+1\\ =2x^2+x-2x-1-x^2+2x+1\\ =x^2+x\\ C=\left(x+y\right)\left(x^2-xy+y^2\right)-x^3\\ =x\left(x^2-xy+y^2\right)+y\left(x^2-xy+y^2\right)-x^3\\ =x^3-x^2y+xy^2+x^2y-xy^2+y^3-x^3\\ =y^3\)
\(D=\left(12x-3\right)\left(x+4\right)-x\left(2x+7\right)\\ =x\left(12x-3\right)+4\left(12x-3\right)-2x^2-7x\\ =12x^2-3x+48x-12-2x^2-7x\\ =10x^2+38x-12\\ E=\left(2x+y\right)\left(4x^2-2xy+y^2\right)\\ =2x\left(4x^2-2xy+y^2\right)+y\left(4x^2-2xy+y^2\right)\\ =8x^3-4x^2y+2xy^2+4x^2y-2xy^2+y^3\\ =8x^3+y^3\)
rút gọn biểu thức
a)2x(2x−1)2−3x(x+3)(x−3)−4x(x+1)2
=2x(4x2-4x+1)-3x.(x2-9)-4x(x2+2x+1)
=8x3-8x2+2x-3x3-27x-4x3-8x2-4x
=8x3-16x2-7x3-29x
\(3x^4-4x^3+2x\left(x^3-2x^2+7x\right)\)
\(=3x^4-4x^3+2x^4-4x^3+14x^2\)
\(=5x^4-8x^3+14x^2\)
3x4 - 4x3 + 2x(x3 - 2x2 + 7x )
= 3x4 - 4x3 + 2x4 _ 4x3 + 14x2
= 5x4 - 8x3 + 14x2