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\(27x^6-8x^3=x^3\left(27x^3-8\right)=x^3\left[\left(3x\right)^3-2^3\right]=x^3\left(3x-2\right)\left(9x^2+6x+4\right)\)
\(x^6-y^6=\left(x^2\right)^3-\left(y^2\right)^3=\left(x^2-y^2\right)\left(x^4+x^2y^2+y^4\right)\)
\(=\left(x-y\right)\left(x+y\right)\left[\left(x^2+y^2\right)^2-x^2y^2\right]\)
\(=\left(x-y\right)\left(x+y\right)\left(x^2+y^2+xy\right)\left(x^2+y^2-xy\right)\)
\(y^9-9x^2y^6+27x^4y^3-27x^6=\left(y^3\right)^3-3.\left(y^3\right)^2.\left(3x^2\right)+3.y^3.\left(3x^2\right)^2-\left(3x^2\right)^3\)
\(=\left(y^3-3x^2\right)^3\)
\(x^3-6x^2+12x-8=0\Leftrightarrow\left(x-2\right)^3=0\Leftrightarrow x=2\)
\(16x^2-9\left(x+1\right)^2=0\Leftrightarrow7x^2-18x-9=0\)
\(\Leftrightarrow\left(x-3\right)\left(7x+3\right)=0\)\(\Rightarrow\orbr{\begin{cases}x=3\\x=\frac{-3}{7}\end{cases}}\)
\(-27+27x-9x^2+x^3=0\Leftrightarrow\left(x-3\right)^3=0\Leftrightarrow x=3\)
a) x^2 - 5x = x .(x-5)
b) x^2 (x+1)-x-1 = x^2(x+1) - (x+1)
= (x+1) . (x^2 - 1)
c) (x-1)^3- 3x(2-x) = x^3 - 3x^2 + 3x + 1 + 3x^2 - 6x
= x^3 - 3x + 1
= x(x^2 - 3 ) + 1
d) 2ab - b^2 = b(2a - b)
e) 9x^2 + 6xy + y = 9x^2 + 6xy + y^2 - y^2 +y
= (3x + y)^2 +y(y - 1)
a) x2 - 5x = x(x-5)
b)x2(x+1)-x-1= x2(x+1)- (x+1)= (x2-1)(x+1)=(x-1)(x+1)(x+1)=(x+1)2(x-1)
d)2ab-b2= b(2a-b)
a, x2+2x+1+x+1
=(x2+2x+2)+x
=(x2+2x+12)+x
=(x+1)2+x
=(2x+1)2
=(2x-1).(2x+1 )
c,xy-y-2x-2
=(xy-2x)-(y-2)
=x.(y-2)-(y-2)
=(y-2).x
e,xy+xz+y2+yz
=(xy+y2)+(xz+yz)
=y.(x+y)+z.(x+y)
=(x+y).(y+z)
d,x3+x2+x+1
=(x3+x2)+(x+1)
=x2.(x+1)+(x+1)
=x2.(x+1)
b,y2+xy+x+2y+1
=(y2+2y)+(xy+x+1)
=y.(y+2) + x.(y+2)
=(y+2).(y+x)
a) 1 - 2y + y2
= (1-y)2
b) ( x + 1 )2 - 25
=( x + 1 )2 - 52
=(x+1+5)(x+1-5)
\(a,x^3+9x^2+27x+27-27z^3\)
\(=\left(x+3\right)^3-\left(3z\right)^3\)
\(=\left(x+3-3z\right)\left(x^2+6x+9+3xz+9z+9z^2\right)\)
.........
\(b,\)
\(=\left(x+1\right)^2\left(x-3\right)+x\left(x-3\right)\)
\(=\left(x-3\right)\left(x^2+3x+1\right)\)
\(c,\)
\(=x^2\left(x^2+10\right)-2x\left(x^2+10\right)\)
\(=x\left(x-2\right)\left(x+10\right)\)