27x³ - 8y³

= ( 3x )³ - ( 2y )³

= ( 3x - 2y ) ( 9x² + 6xy + 4y² )

.....

27x³-8y³

=(3x)³-(2y)³

=(3x-2y)(9x²+6xy+4y²)

\(27x^3-8y^3=\left(3x\right)^3-\left(2y\right)^3=\left(3x-2y\right)\left(9x^2+6xy+4y^2\right)\)

\(8-27x^3\)

\(=2^3-\left(3x\right)^3\)

\(=\left(2-3x\right)\left(4+6x+9x^2\right)\)

a) \(8-27x^3=\left(2-x\right)\left(4+6x+9x^2\right)\)

b) \(27+27x+9x^2+x^3=\left(3+x\right)^3\)

c) \(x^3+8y^3=\left(x+2y\right)\left(x^2-2xy+4y^2\right)\)

a) 9x⁴+16y⁶-24x²y³

=(3x²)²-2.3x².4y³+(4y³)²

=(3x²-4y³)²

b) 16x²-24xy+9y²

=(4x)²-2.4x.3y+(3y)²

=(4x-3y)²

c) 36x²-(3x-2)²

=(36x-3x+2)(36x+3x-2)

=(33x+2)(39x-2)

d) 27x³+54x²y+36xy²+8y³

=(3x)³+3.(3x)².2y+3.3x.(2y)²+(2y)³

=(3x+2y)³

e) y⁹-9x²y⁶+27x⁴y³-27x⁶

=(y³)³-3.(y³)².3x²+3.y³.(3x²)²-(3x²)³

=(y³-3x²)³

f) 64x³+1

= (4x)³+1³

=(4x+1)[(4x)²-4x.1+1²]

=(4x+1)(16x²-4x+1)

e) 27x⁶-8x³  *sửa đề*

=(3x²)³-(2x)³

=(3x²-2x)[(3x)²+3x².2x+(2x)²]

=(3x²-2x)(9x²+6x³+4x²)

~~~

Trả lời:

2, 8x²y - 8y = 8y ( x² - 1 ) = 8y ( x - 1 )( x + 1 )

3, 24x³ - 3 = 3 ( 8x³ - 1 ) = 3 ( 2x - 1 )( 4x² + 2x + 1 )

4, 4x² - 4y² = ( 2x )² - ( 2y )² = ( 2x - 2y )( 2x + 2y )

5, x⁵ + 27x² = x² ( x³ + 27 ) = x² ( x + 3 )( x² - 3x + 9 )

\(\left(x-1\right)^2-25\)

\(=x^2-2x+1-25\)

\(=x^2-2x-24\)

\(=x^2-6x+4x-24\)

\(=x.\left(x-6\right)+4.\left(x-6\right)\)

\(=\left(x+4\right).\left(x-6\right)\)

a, \(1-2y+y^2=\left(y+1\right)^2=\left(y+1\right)\left(y+1\right)\)

b, \(\left(x+1\right)^2-25=\left(x+1\right)^2-5^2=\left(x+1-5\right)\left(x+1+5\right)=\left(x-4\right)\left(x+6\right)\)

c, \(1-4x^2=1^2-\left(2x\right)^2=\left(1-2x\right)\left(1+2x\right)\)

d,  \(8-27x^3=2^3-\left(3x\right)^3=\left(2-3x\right)\left(4+6x+9x^2\right)\)

\(27x^3-27x^2+18x-4\)

\(=27x^3-9x^2-18x^2+6x+12x-4\)

\(=9x^2\left(3x-1\right)-6x\left(3x-1\right)+4\left(3x-1\right)\)

\(=\left(9x^2-6x+4\right)\left(3x-1\right)\)

\(27x^3-27x^2+18x-4\\=27x^3-9x^2-18x^2+6x+12x-4\\=9x^2(3x-1)-6x(3x-1)+4(3x-1)\\=(3x-1)(9x^2-6x+4)\)

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) \(1-9x+27x^2-27x^3\)

\(=-\left(27x^3-27x^2+9x-1\right)\)

\(=-\left(3x-1\right)^3\)

d) \(x^3+\frac{3}{2}x^2+\frac{3}{4}x+\frac{1}{8}\)

\(=\left(x+\frac{1}{2}\right)^3\)

e) \(27x^3-54x^2y+36xy^2-8y^3\)

\(=\left(3x-2y\right)^3\)

a, \(x^3-3x^2+3x-1=\left(x-1\right)^3\)

b, \(1-9x+27x^2-27x^3=-\left(3x-1\right)^3\)

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a) \(x^3-x=x\left(x^2-1\right)=x\left(x+1\right)\left(x-1\right)\)

\(b,y^2+2y+1-x^2=\left(y+1\right)^2-x^2=\left(y+1+x\right)\left(y+1-x\right)\)

\(c,27x^3+8y^3=\left(3x+2y\right)\left(9x^2-6xy+4y^2\right)\) 

\(f,x\left(x-3\right)-x+3=\left(x-1\right)\left(x-3\right)\)

\(a.x^3-x=x\left(x^2-1\right)=x\left(x+1\right)\left(x-1\right)\)

\(b.y^2+2y=1-x^2=\left(y+1\right)^2-x^2=\left(y+1+x\right)\left(y+1-x\right)\)

\(c.27^3+8y^3=\left(3x+2y\right)\left(9^2x-6xy+4y\right)\)

\(f.x\left(x-3\right)-x+3=\left(x-1\right)\left(x-3\right)\)

~Study well~ :)