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Làm thế này nha
\(\frac{27x^3-1}{3x-1}=\frac{\left(3x\right)^3-1}{3x-1}=\frac{\left(3x-1\right)\left(9x^2+3x+1\right)}{3x-1}=9x^2+3x+1\)
Ta có: \(\left(27x^3-1\right):\left(3x-1\right)=\left[\left(3x\right)^3-1^3\right]:\left(3x-1\right)=\left(3x-1\right)\left(9x^2+3x+1\right):\left(3x-1\right)=9x^2+3x+1\)
Với đề bài và đã có x ta chỉ cần thay x vào là được :
\(101^3-3.101^2+3.101-1=\)
\(97^3+9.97^2+27.97+27=\)
Dùng hằng đẳng thức đi bạn :)
a)\(x^3-3x^2+3x-1=\left(x-1\right)^3=\left(101-1\right)^3=100^3=1000000\)
b)\(x^3+9x^2+27x+27=\left(x+3\right)^3=\left(97+3\right)^3=100^3=1000000\)
a) \(x^3+6x^2+12x+8\)
\(=\left(x+2\right)^3\)
b) \(x^3-3x^2+3x-1\)
\(=\left(x-1\right)^3\)
c) \(1-9x+27x^2-27x^3\)
\(=-\left(27x^3-27x^2+9x-1\right)\)
\(=-\left(3x-1\right)^3\)
a ) \(\left(4x^2-9y^2\right):\left(2x-3y\right)\)
\(=\left(2x-3y\right)\left(2x+3y\right);\left(2x-3y\right)\)
\(=2x+3y\)
b ) \(\left(27x^3-1\right):\left(3x-1\right)\)
\(=\left(3x-1\right)\left(9x^2+3x+1\right):\left(3x-1\right)\)
\(=9x^2+3x+1\)
a) (4x2 – 9y2) : (2x – 3y);
=(2x-3y)(2x+3y):(2x-3y)
=2x+3y
b) (27x3 – 1) : (3x – 1);
=(3x-1)(9x2+3x+1):(3x-1)
=9x2+3x+1
c) (8x3 + 1) : (4x2 – 2x + 1);
=(2x+1)(4x2-2x+1):(4x2-2x+1)
=2x+1
d) (x2 – 3x + xy -3y) : (x + y)
=[x.(x-3)+y.(x-3)]:(x+y)
=(x-3)(x+y):(x+y)
=x-3
a) (4x2 – 9y2) : (2x – 3y);
=(2x-3y)(2x+3y):(2x-3y)
=2x+3y
b) (27x3 – 1) : (3x – 1);
=(3x-1)(9x2+3x+1):(3x-1)
=9x2+3x+1
c) (8x3 + 1) : (4x2 – 2x + 1);
=(2x+1)(4x2-2x+1):(4x2-2x+1)
=2x+1
d) (x2 – 3x + xy -3y) : (x + y)
=[x.(x-3)+y.(x-3)]:(x+y)
=(x-3)(x+y):(x+y)
=x-3
a) ( 4x^2 - 9y^2) : ( 2x- 3y) = ( 2x - 3y)(2x + 3y) : (2x- 3y) = 2x + 3y
b) (27x^3 - 1 ) : (3x- 1) = ( 3x - 1 )(9x^2 + 3x + 1 ) : ( 3x - 1 ) = 9x^2 + 3x+ 1
c) ( 9x^3 + 1 ) : (4x^2 - 2x + 1 ) = ( 2x + 1 )(4x^2 - 2x + 1 ) : (4x^2 - 2x + 1 ) = 2x+ 1
d) ( x^2 - 3x + x y - 3y ) : ( x+ y)
= [ x(x- 3 ) + y ( x - 3 ) ] : ( x+ y)
= ( x+ y)(x- 3 ) : ( x+ y)
=x - 3
\(\frac{27x^3-1}{3x-1}=\frac{\left(3x\right)^3-1}{3x-1}=\frac{\left(3x-1\right)\left(9x^2+3x+1\right)}{3x-1}=9x^2+3x+1\)
ủng hộ 1 t i c k nha cảm ơn
=[(3x)^3-1] : ( 3x-1)
=(3x-1).[9(x)^2+3x+1] : (3x-1)
= 9.x^2+3x+1