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Bài 1 :
a, \(\left(x+3\right)^2+\left(x-3\right)^2+2\left(x^2-9\right)\)
\(=x^2+6x+9+x^2-6x+9+2x^2-18\)
\(=4x^2\)
b, \(\left(4x-1\right)^3-\left(4x-3\right)\left(16x^2+3\right)\)
\(=64x^3-32x^2+4x-16x^2+8x-1-64x^3-12x+48x^2+9=8\)
a) 5x2 ( 3x2 -7x+2)-15x(x-3)
=15x4-35x3+10x2-15x2+45x
=15x4-35x3-5x2+45x
c) (x+3)(x-3)(x-2)(x+1)
=(x2-9)(x2+x-2x-2)
=(x2-9)(x2-x-2)
=x4-x3-2x2-9x2+9x+18
=x4-x3-11x2+9x+18
d)(2x+1)2+(4x-1)2+2(2x+1)(4x+1)
=2x2+4x+1-16x2-8x+1
=2x2+4x+1-16x2-8x+1+16x2-4x+8x-2
=2x2+7
e) (2x2-3x)(5x2-2x+1)-10x2(x+3)
=10x4 -4x3+2x2-15x3+6x2-3 -10x2-30x
=10x4-19x3-2x2-30x-3
1) ĐKXĐ: x \(\ne\)1; x \(\ne\)0
Ta có: A = \(\frac{4x^2-3x+17}{x^3-1}+\frac{2x-1}{x^2+x+1}+\frac{6x}{x-x^2}\)
A = \(\frac{4x^2-3x+17}{\left(x-1\right)\left(x^2+x+1\right)}+\frac{\left(2x-1\right)\left(x-1\right)}{\left(x-1\right)\left(x^2+x+1\right)}-\frac{6x}{x\left(x-1\right)}\)
A = \(\frac{4x^2-3x+17}{\left(x-1\right)\left(x^2+x+1\right)}+\frac{2x^2-2x-x+1}{\left(x-1\right)\left(x^2+x+1\right)}-\frac{6\left(x^2+x+1\right)}{\left(x-1\right)\left(x^2+x+1\right)}\)
A = \(\frac{4x^2-3x+17+2x^2-3x+1-6x^2-6x-6}{\left(x-1\right)\left(x^2+x+1\right)}\)
A = \(\frac{-12x+12}{\left(x-1\right)\left(x^2+x+1\right)}\)
A = \(\frac{-12\left(x-1\right)}{\left(x-1\right)\left(x^2+x+1\right)}=-\frac{12}{x^2+x+1}\)
b) Ta có: B = \(\frac{x+9y}{x^2-9y^2}-\frac{3y}{x^2+3xy}\)
B = \(\frac{x+9y}{\left(x-3y\right)\left(x+3y\right)}-\frac{3y}{x\left(x+3y\right)}\)
B = \(\frac{x\left(x+9y\right)}{x\left(x-3y\right)\left(x+3y\right)}-\frac{3y\left(x-3y\right)}{x\left(x+3y\right)\left(x-3y\right)}\)
B = \(\frac{x^2+9xy-3xy+9y^2}{x\left(x-3y\right)\left(x+3y\right)}\)
B = \(\frac{x^2+6xy+9y^2}{x\left(x-3y\right)\left(x+3y\right)}\)
B = \(\frac{\left(x+3y\right)^2}{x\left(x-3y\right)\left(x+3y\right)}\)
B = \(\frac{x+3y}{x\left(x-3y\right)}\)
\(A=\frac{4x^2-3x+17}{x^3-1}+\frac{2x-1}{x^2+x+1}+\frac{6x}{x-x^2}\)
\(A=\frac{4x^2-3x+17}{\left(x-1\right)\left(x^2+x+1\right)}+\frac{2x-1}{x^2+x+1}+\frac{6x}{x\left(1-x\right)}\)
\(A=\frac{4x^2-3x+17}{\left(x-1\right)\left(x^2+x+1\right)}+\frac{2x-1}{x^2+x+1}-\frac{6x}{x\left(x-1\right)}\)
\(A=\frac{x\left(4x^2-3x+17\right)+x\left(x-1\right)\left(2x-1\right)-6x\left(x^2+x+1\right)}{x\left(x-1\right)\left(x^2+x+1\right)}\)
\(A=\frac{4x^3-3x^2+17x+x\left(2x^2-x-2x+1\right)-6x^3-6x^2-6x}{x\left(x-1\right)\left(x^2+x+1\right)}\)
\(A=\frac{\left(4x^3+2x^3-6x^3\right)-3x^2-3x^3-6x^2+17x+x-6x}{x\left(x-1\right)\left(x^2+x+1\right)}\)
\(A=\frac{-12x^2+12x}{x\left(x-1\right)\left(x^2+x+1\right)}\)
\(A=\frac{-12x\left(x-1\right)}{x\left(x-1\right)\left(x^2+x+1\right)}=\frac{-12}{x^2+x+1}\)
\(a,3x^3-6x^2+3x\)
\(=3x\left(x^2-2x+1\right)\)
\(=3x\left(x-1\right)^2\)
\(b,16x^2y-4xy^2-4x^3\)
\(=-4x\left(x^2-4xy+4y^2-3y^2\right)\)
\(=-4x\left(x-2y+y\sqrt{3}\right)\left(x-2y-y\sqrt{3}\right)\)
\(a,\left(x-3y\right)\left(x^2+3xy+9y^2\right)=x^3-27y^3\)
\(b,\left(x^2-3\right)\left(x^4+3x^2+9\right)=x^6-27\)
\(c,\left(x+2y+z\right)\left(x+2y-z\right)=\left(x+2y\right)^2-z^2\)
\(=x^2+4xy+4y^2-z^2\)
\(d,\left(2x-1\right)\left(4x^2+2x+1\right)=8x^3-1\)
\(e,\left(5+3x\right)^3=125+225x+135x^2+27x^3\)
\(a,\dfrac{x^3-x}{3x+3}=\dfrac{x\left(x^2-1\right)}{3\left(x+1\right)}=\dfrac{x\left(x-1\right)\left(x+1\right)}{3\left(x+1\right)}=\dfrac{x\left(x-1\right)}{3}\\ b,\dfrac{x^2+3xy}{x^2-9y^2}=\dfrac{x\left(x+3y\right)}{\left(x-3y\right)\left(x+3y\right)}=\dfrac{x}{x-3y}\\ c,\dfrac{x^2+4x+4}{3x+6}=\dfrac{\left(x+2\right)^2}{3\left(x+2\right)}=\dfrac{x+2}{3}\)