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Bài 1: Thực hiện phép tính
a) 3x(2x2 - 5x + 9) = \(6x^3-15x^2+27x\)
b) 5x(x2-xy+1) = \(5x^3-5xy+5x\)
c) -2/3x2y(3xy-x2+y) = \(-2x^3y^2+\dfrac{2}{3}x^4y-\dfrac{2}{3}x^2y^2\)
2) Thực hiện phép tính
a) (5x-2y) (x2-xy+1) = \(5x^3+5x-7y-2x^3y+2xy^2\)
b) (x+3y)(x2-2xy+y) = \(x^3-x^2y+xy+6xy^2+y^2\)
c) (3x-5y) (4x+ 7y) = \(12x^2-xy-35y^2\)
Bài 3: Rút gọn các biểu thức sau(bằng cách khai triển hằng đẳng thức):
a) (x+y)2+(x-y)2
= \(x^2+2xy+y^2+x^2-2xy+y^2\)
= \(\left(x^2+x^2\right)+\left(2xy-2xy\right)+\left(y^2+y^2\right)\)
= \(2x^2+2y^2=2\left(x^2+y^2\right)\)
b) (x+2)(x-2)-(x-3)(x+1)
= \(x^2-4\) - \(\left(x^2-2x-3\right)\)= \(x^2-4-x^2+2x+3\)
= \(\left(x^2-x^2\right)+2x+\left(-4+3\right)\)=\(2x-1\)
c) (x-2)(x+2)-(x-2)2
=>\(x^2-4-\left(x^2-2.x.2+2^2\right)=x^2-4-x^2-4x+4=\left(x^2-x^2\right)+\left(-4+4\right)-4x=-4x\)
d) (2x+y)(4x2-2xy+y2)-(2x-y)(4x2+2xy+y2)
= \(8x^3+y^3-\left(8x^3-y^3\right)\)
= \(8x^3+y^3-8x^3+y^3\)
= \(\left(8x^3-8x^3\right)+\left(y^3+y^3\right)\)= \(2y^3\)
1a : x = -1
2a : x = 10
còn mấy bài khác mình không biết giải nha
a: \(=\dfrac{4x^2+4x+1-4x^2+4x-1}{\left(2x+1\right)\left(2x-1\right)}\cdot\dfrac{5\left(2x-1\right)}{4x}\)
\(=\dfrac{8x\cdot5}{4x\left(2x+1\right)}=\dfrac{10}{2x+1}\)
b: \(=\left(\dfrac{1}{x^2+1}+\dfrac{x-2}{x+1}\right):\dfrac{1+x^2-2x}{x}\)
\(=\dfrac{x+1+x^3+x-2x^2-2}{\left(x+1\right)\left(x^2+1\right)}\cdot\dfrac{x}{\left(x-1\right)^2}\)
\(=\dfrac{x^3-2x^2+2x-1}{\left(x+1\right)\left(x^2+1\right)}\cdot\dfrac{x}{\left(x-1\right)^2}\)
\(=\dfrac{\left(x-1\right)\left(x^2-x+1\right)}{\left(x+1\right)\left(x^2+1\right)}\cdot\dfrac{x}{\left(x-1\right)^2}\)
\(=\dfrac{x\left(x^2-x+1\right)}{\left(x^2-1\right)\left(x^2+1\right)}\)
c: \(=\dfrac{1}{x-1}-\dfrac{x^3-x}{x^2+1}\cdot\left(\dfrac{1}{\left(x-1\right)^2}-\dfrac{1}{\left(x-1\right)\left(x+1\right)}\right)\)
\(=\dfrac{1}{x-1}-\dfrac{x\left(x-1\right)\left(x+1\right)}{x^2+1}\cdot\dfrac{x+1-x+1}{\left(x-1\right)^2\cdot\left(x+1\right)}\)
\(=\dfrac{1}{x-1}-\dfrac{x}{x^2+1}\cdot\dfrac{2}{\left(x-1\right)}\)
\(=\dfrac{x^2+1-2x}{\left(x-1\right)\left(x^2+1\right)}=\dfrac{x-1}{x^2+1}\)
a ) \(\left(x+1\right)\left(x-2\right)=x^2-2x+x-2=x^2-x-2\)
b ) \(\left(4x^4y^4-12x^2y^2\right):4x^2y^2=x^2y^2-3\)
c ) \(\frac{3x^2-1}{2x}+\frac{x^2+1}{2x}=\frac{3x^2-1+x^2+1}{2x}=\frac{4x^2}{2x}=2x\)
d ) \(\frac{x^2}{x-1}+\frac{2x}{1-x}+\frac{1}{x-1}=\left(\frac{x^2}{x-1}+\frac{1}{x-1}\right)+\frac{2x}{1-x}\)
\(=\frac{x^2+1}{x-1}+\frac{2x}{1-x}=\frac{x^2+1}{x-1}+\frac{-2x}{x-1}=\frac{x^2+1-2x}{x-1}=\frac{\left(x-1\right)^2}{x-1}=x-1\)
a) .......=x2-x-2
b) .........=x2y2-3
c) .......=(3x2-1+x2+1)/2x=4x2/2x=2x
d) x2 /(x-1)+(-2x)/(x-1)+1/(x-1)=(x2-2x+1)/(x-1)=(x-1)2/(x-1)=x-1
e)...
x-y=4
=> x2-2xy+y2=16
<=> 106-2xy =16 (vì x2+y2 =106)
=>xy=(106-16)/2=45
ta có x3 -y3 =(x-y)(x2+xy+y2 )
=4(106+45)=604
A = ( x + 1 )( x2 - 3x - 2 ) + ( x + 1 )( x2 - x + 1 )
= ( x + 1 )[ ( x2 - 3x - 2 ) + ( x2 - x + 1 ) ]
= ( x + 1 )( x2 - 3x - 2 + x2 - x + 1 )
= ( x + 1 )( 2x2 - 4x - 1 )
= x( 2x2 - 4x - 1 ) + 2x2 - 4x - 1
= 2x3 - 4x2 - x + 2x2 - 4x - 1
= 2x3 - 2x2 - 5x - 1
B = ( x - y )( x2 + xy + y2 ) - ( x + y )( x2 + 2x + y2 )
= x3 - y3 - ( x3 + 2x2 + xy2 + x2y + 2xy + y3 )
= x3 - y3 - x3 - 2x2 - xy2 - x2y - 2xy - y3
= -2y3 - 2x2 - xy2 - x2y - 2xy
a) \(A=\left(x+1\right)\left(x^2-3x-2\right)+\left(x+1\right)\left(x^2-x+1\right)\)
\(=x.x^2-x.3x-x.2+1.x^2-1.3x-1.2+x.x^2-x.x+x.1+1.x^2-1.x+1.1\)
\(=x^3-3x^2-2x+x^2-3x-2+x^3-x^2+x+x^2-x+1\)
\(=\left(x^3+x^3\right)+\left(-3x^2+x^2-x^2+x^2\right)+\left(-2x-3x+x-x\right)+\left(-2+1\right)\)
\(=2x^3-2x^2-5x-1\)
b) \(B=\left(x-y\right)\left(x^2+xy+y^2\right)-\left(x+y\right)\left(x^2+2x+y^2\right)\)
\(=x.x^2+x.xy+x.y^2-y.x^2-y.xy-y.y^2-x.x^2-x.2x-x.y^2+y.x^2+y.2x+y.y^2\)
\(=x^3+x^2y+xy^2-x^2y-xy^2-y^3-x^3-2x^2-xy^2+xy^2+2xy+y^3\)
\(=\left(x^3-x^3\right)+\left(x^2y-x^2y\right)+\left(xy^2-xy^2-xy^2+xy^2\right)-2x^2+2xy+\left(-y^3+y^3\right)\)
\(=-2x^2+2xy\)