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a) \(\left(x^2-1\right)\left(x^2+2x\right)=x^4+2x^3-x^2-2x\)
b) \(\left(2x-1\right)\left(3x+2\right)\left(3-x\right)=6x^2-3x+4x-2\left(3-x\right)\)
\(=6x^2-3x+4x-6+2x\)
\(=6x^2+3x-6\)
c) \(\left(x+3\right)\left(x^2+3x-5\right)=x^3+3x^2+3x^2+9x-5x-15\)
\(=x^3+6x^2+4x-15\)
d) \(\left(x+1\right)\left(x^2-x+1\right)=x^3+x^2-x^2-x+x+1\)
\(=x^3+1\)
e) \(\left(2x^3-3x-1\right)\left(5x+2\right)=10x^4-15x^2-5x+4x^3-6x-2\)
\(=10x^4+4x^3-15x^2-11x-2\)
f) \(\left(x^2-2x+3\right)\left(x-4\right)=x^3-2x^2+3x-4x^2+8x-12\)
\(=x^3-6x^2+11x-12\)
\(a,\left(3x+x\right)\left(x^2-9\right)-\left(x-3\right)\left(x^2+3x+9\right)\)
\(=4x\left(x^2-9\right)-x^3+27\)
\(=4x^3-36x-x^3+27\)
\(=3x^3-36x+27\)
\(\left(x+6\right)^2-2x.\left(x+6\right)+\left(x-6\right).\left(x+6\right)\)
\(=\left(x+6\right).\left(x+6-2x+x-6\right)\)
\(=\left(x+6\right).0\)
\(=0\)
a: \(=x^3-5x^2-x^2+10x+\dfrac{3}{2}x-15=x^3-6x^2+\dfrac{23}{2}x-15\)
b: \(=5x^3-x^4-10x^2+2x^3+5x-x^2-5+x\)
\(=-x^4+7x^3-11x^2+6x-5\)
c: \(=\dfrac{x^3-3x^2+2x^2-6x-x+3}{x-3}=x^2+2x-1\)
a) 2(x-1)2 - 4(x+3)2 + 2x(x-5)
= 2(x2 -2x +1)- 4(x2 + 6x +9) + 2x2 -10x
= 2x2 - 4x + 2 -4x2 - 24x - 36 + 2x2 - 10x
= (2x2 + 2x2 - 4x2) - (4x + 24x+10x) +(2-36)
= -38x-34
b) 2(2x+5)2 -3(4x+1)(1-4x)
= 2(4x2 + 20x + 25) + 3(4x+1)(4x-1)
= 8x2 +40x + 50 + 3(16x2 -1)
= 8x2 + 40x + 50 + 48x2 - 3
=56x2 +40x + 47
a, \(2\left(x-1\right)^2-4\left(x+3\right)^2+2x\left(x-5\right)\)
\(=2\left(x^2-2x+1\right)-4\left(x^2+6x+9\right)+2x\left(x-5\right)\)
\(=2x^2-4x+2-4x^2-24x-36+2x^2-10=-28x-44\)
b, \(2\left(2x+5\right)^2-3\left(4x+1\right)\left(1-4x\right)\)
\(=2\left(4x^2+20x+25\right)-3\left(1-16x^2\right)\)
\(=8x^2+40x+50-3+48x^2=56x^2+40x+47\)
Bài 1:
b: \(=\dfrac{x+3-4-x}{x-2}=\dfrac{-1}{x-2}\)
Bài 2:
a: \(=\dfrac{x+1}{2\left(x+3\right)}+\dfrac{2x+3}{x\left(x+3\right)}\)
\(=\dfrac{x^2+x+4x+6}{2x\left(x+3\right)}=\dfrac{x^2+5x+6}{2x\left(x+3\right)}=\dfrac{x+2}{2x}\)
d: \(=\dfrac{3}{2x^2y}+\dfrac{5}{xy^2}+\dfrac{x}{y^3}\)
\(=\dfrac{3y^2+10xy+2x^3}{2x^2y^3}\)
e: \(=\dfrac{x^2+2xy+x^2-2xy-4xy}{\left(x+2y\right)\left(x-2y\right)}=\dfrac{2x^2-4xy}{\left(x+2y\right)\cdot\left(x-2y\right)}=\dfrac{2x}{x+2y}\)
a: \(=\dfrac{2\left(x+2\right)\left(x-1\right)}{x+2}=2x-2\)
b: \(=\dfrac{2x^3+x^2-6x^2-3x+2x+1}{2x+1}=x^2-3x+1\)
c: \(=\dfrac{x^3+2x^2-2x^2-4x+2x+4}{x+2}=x^2-2x+2\)
d: \(=\dfrac{x^2\left(x-3\right)}{x-3}=x^2\)
a. =4x^2-9-6x^2+3x
=-2x^2-9+3x
B. [x+3-(x-3)]^2
=6^2=36