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a) ( 5x - y )( 25x2 + 5xy + y2 ) = ( 5x )3 - y3 = 125x3 - y3
b) ( x - 3 )( x2 + 3x + 9 ) - ( 54 + x3 ) = x3 - 33 - 54 - x3 = -27 - 54 = -81
c) ( 2x + y )( 4x2 - 2xy + y2 ) - ( 2x - y )( 4x2 + 2xy + y2 ) = ( 2x )3 + y3 - [ ( 2x )3 - y3 ]= 8x3 + y3 - 8x3 + y3 = 2y3
d) ( x + y )2 + ( x - y )2 + ( x + y )( x - y ) - 3x2 = x2 + 2xy + y2 + x2 - 2xy + y2 + x2 - y2 - 3x2 = y2
e) ( x - 3 )3 - ( x - 3 )( x2 + 3x + 9 ) + 6( x + 1 )2
= x3 - 9x2 + 27x - 27 - ( x3 - 33 ) + 6( x2 + 2x + 1 )
= x3 - 9x2 + 27x - 27 - x3 + 27 + 6x2 + 12x + 6
= -3x2 + 39x + 6
= -3( x2 - 13x - 2 )
f) ( x + y )( x2 - xy + y2 ) + ( x - y )( x2 + xy + y2 ) - 2x3
= x3 + y3 + x3 - y3 - 2x3
= 0
g) x2 + 2x( y + 1 ) + y2 + 2y + 1
= x2 + 2x( y + 1 ) + ( y2 + 2y + 1 )
= x2 + 2x( y + 1 ) + ( y + 1 )2
= ( x + y + 1 )2
= [ ( x + y ) + 1 ]2
= ( x + y )2 + 2( x + y ) + 1
= x2 + 2xy + y2 + 2x + 2y + 1
Bạn viết rõ hơn nhé :
\(\frac{x^4-xy^3}{2xy+y^2}:\frac{x^3+x^2y+xy^2}{2x+y}\)
= \(\frac{x^4-xy^3}{2xy+y^2}.\frac{2x+y}{x^3+x^2y+xy^2}\)
= \(\frac{x.\left(x-y\right).\left(x^2+xy+y^2\right).\left(2x+y\right)}{y.\left(2x+y\right).x.\left(x^2+xy+y^2\right)}\)
= \(\frac{x-y}{y}\)
Chúc bạn học tốt !!!
a)<=>
A,=(x+y)(x-y)=x^2-y^2
x=(-1/2)^5:(1/2)^4=-1/2
x^2=1/4
y=8^2/(-2)^5=-2
y^2=4
A=1/4-4=-15/4
\(a,\left(x-3\right)\left(x^2+3x+9\right)-\left(x^2-1\right)\left(x+27\right)\)
\(=\left(x^3-27\right)-x^3-27x^2+x+27=x-27x^2\)
\(b,\left(3-x\right)^3-\left(x+3\right)\left(x^2-3x+9\right)\)
\(=27-9x+3x^2-x^3-\left(x^3+27\right)=3x^2-9x-2x^3\)
\(c,\left(x-2\right)\left(x^2+2x+4\right)-x\left(x-3\right)\left(x+3\right)\)
\(=\left(x^3-8\right)-x\left(x^2-9\right)=x^3-8-x^3+9x=9x-8\)
a) (x-3)(x2+3x+9)-(x2-1)(x+27)
=(x3-27)-(x3+27x2-x-27)
=x3-27-x3-27x2+x+27
=-27x2+x
=x(-27x+1)
b) (3-x)3-(x+3)(x2-3x+9)
=27-27x+9x2-x3-x3-27
=-2x3+9x2-27x
=x(-2x+9x-27)
c) (x-2)(x2+2x+4)-x(x-3)(x+3)
=x3-8-x(x2-9)
=x3-8-x3+9x
=9x-8
#H
\(1,\)
\(\left(x^2-9y^2\right)\left(4x+12y\right)\)
\(=\left(x-3y\right)\left(x+3y\right)-4\left(x+3y\right)\)
\(=\left(x+3y\right)\left(x-3y-4\right)\)
\(3,\)
\(-x^2+2xy-y^2+25\)
\(=-\left(x^2-2xy+y^2\right)+25\)
\(=25-\left(x-y\right)^2\)
\(=5^2-\left(x-y\right)^2\)
\(=\left(5-x+y\right)\left(5+x-y\right)\)
\(a,x^2+7x+7y-y^2\)
\(=x^2-y^2+7\left(x+y\right)\)
\(=\left(x-y\right)\left(x+y\right)+7\left(x+y\right)\)
\(=\left(x+y\right)\left(x-y+7\right)\)
\(b,x^2-2x-9y^2+6y\)
\(=x^2-\left(3y\right)^2-2\left(x-3y\right)\)
\(=\left(x-3y\right)\left(x+3y\right)-2\left(x-3y\right)\)
\(=\left(x-3y\right)\left(x+3y-2\right)\)
\(c,x^2-xy+x^3-3x^{2y}+3x^{2y}-y^3\)
\(=x\left(x-y\right)+\left(x-y\right)\left(x^2+xy+y^2\right)\)
\(=\left(x-y\right)\left(x+x^2+xy+y^2\right)\)
h, \(27x^3-8=\left(3x-2\right)\left(9x^2+6x+4\right)\)
\(\Rightarrow\left(27x^3-8\right):\left(3x-2\right)\\ =\left(3x-2\right)\left(9x^2+6x+4\right):\left(3x-2\right)\\ =9x^2+6x+4\)
g, \(x^4-2x^2+1=\left(x^2-1\right)^2\)
\(\Rightarrow\left(x^4-2x^2+1\right):\left(1-x^2\right)\\ =\left(x^2-1\right)^2:\left(1-x^2\right)\\ =x^2-1\)
a, \(2x\left(x+2\right)-\left(x+2\right)\left(x-2\right)=\left(x+2\right)^2=x^2+4x+4\)
b, \(\left(x-3\right)\left(x^2+3x+9\right)-\left(x^2-27x\right)=x^3-27-x^2+27x\)
c, \(\left(x+y\right)\left(x^2-xy+y^2\right)-\left(x-y\right)\left(x^2+xy+y^2\right)=x^3+y^3-x^3+y^3=2y^3\)
2𝑥(𝑥+2)−(𝑥+2)(𝑥−2)
2𝑥^2+4𝑥−(𝑥+2)(𝑥−2)
2𝑥^2+4𝑥−(𝑥(𝑥−2)+2(𝑥−2))
2𝑥^2+4𝑥−(𝑥^2−2𝑥+2(𝑥−2))
2𝑥^2+4𝑥−(𝑥^2−2𝑥+2𝑥−4)
2𝑥^2+4𝑥−(𝑥^2−4)
2𝑥^2+4𝑥−𝑥^2+4
2𝑥^2−𝑥^2+4𝑥+4