\(x^3-y^3-36xy\)

\(=\left(x-y\right)^3+3xy\left(x-y\right)-36xy\)

\(=12^3+36xy-36xy\)

\(=1728\)

Bài 1 : 

a) \(x^4-4x^2-4x-1\)

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

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

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

b) \(x^2+2x-15\)

\(=x^2+2x+1-16\)

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

\(=\left(x+1+4\right)\left(x+1-4\right)=\left(x+5\right)\left(x-3\right)\)

c) \(x^3y-2x^2y^2+5xy\)

\(=xy\left(x^2-2xy+5\right)\)

B2:

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

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

\(=2x^2-4x+2-4x^2+9\)

\(=-2x^2-4x+11\)

b) \(\left(x+3\right)^2-2\left(x+3\right)\left(x-3\right)+\left(x-3\right)^2\)

\(=\left(x+3-x+3\right)^2=6^2=36\)

c) \(4\left(x-1\right)\left(x+3\right)+5\left(2x+1\right)^2-2\left(5-3x\right)^2\)

\(=4\left(x^2+2x-3\right)+5\left(4x^2+4x+1\right)-2\left(9x^2-30x+25\right)\)

\(=4x^2+8x-12+20x^2+20x+5-18x^2+60x-50\)

\(=6x^2+88x-57\)

Mình sửa: Bài 1
2)x²+3x-15

a) x² + 6x + 9 = x² + 2 . x . 3 + 3² = (x + 3)²

b) 10x – 25 – x² = -(-10x + 25 +x²) = -(25 – 10x + x²)

                         = -(5² – 2 . 5 . x – x²) = -(5 – x)²

c) 8x³ - 1/8 = (2x)³ – (1/2)³ = (2x - 1/2)[(2x)² + 2x . 12 + (1/2)²]

                    ^{= (2x - 1/2)(4x2 + x + 1/4)} 

d)1/25x² – 64y² = (1/5x)2(1/5x)2- (8y)² = (1/5x + 8y)(1/5x - 8y)

Bài 1: 4a²-4ab+b²-9a²b²

=(2a)²-2.2a.b+b²-(3ab)²

=(2a-b)²-(3ab)²

=(2a-b-3ab)(2a-b+3ab)

a/ (4a²-4ab+b²)-9a²b²

= (2a-b)²-(3ab)²

= (2a-b-3ab) (2a-b+3ab) 

\(a)\) \(3x^2-6x=3x\left(x-2\right)\)

\(b)\) \(9x^3-9x^2y-4x+4y\)

\(=9x^2.\left(x-y\right)-4\left(x-y\right)\)

\(=\left(9x^2-4\right)\left(x-y\right)\)

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

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

\(c)\) \(x^3-2x^2-8x\)

\(=x\left(x^2-2x-8\right)\)

\(=x\left(x+2\right)\left(x-4\right)\)

1.

a) \(\left(-2x^3\right)\)\(\left(x^2+5x-\frac{1}{2}\right)\) = \(-2x^5\)\(-10x^4\) \(+x^3\)

b) (\(6x^3-7x^2\)\(-x+2\))\(:\left(2x+1\right)\)=\(3x^2-5x+2\)

2.

a) 9x(3x-y) + 3y (y-3x)=9x(3x-y)-3y(3x-y)

= (9x-3y)(3x-y)

= 3(3x-y)(3x-y)

= 3(3x-y)^2

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

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

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

= \(\left(x+3\right)\left(x-3\right)\left(x-3\right)\)

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

Bài 1 ) a ) \(\left(-2x^3\right)\left(x^2+5x-\frac{1}{2}\right)\)

\(=-2x^5-10x^4+x^3\)

b ) \(\left(6x^3-7x^2+x+2\right):\left(2x+1\right)\)

\(=3x^2-5x+2\)

2 ) a ) \(9x\left(3x-y\right)+3y\left(y-3x\right)\)

\(=9x\left(3x-y\right)-3y\left(3x-y\right)\)

\(=\left(3x-y\right)\left(9x-3y\right)\)

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

b ) \(x^3-3x^2-9x+27\)

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

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

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

\(=\left(x-3\right)\left(x+3\right)\left(x-3\right)\)

Bài làm

a) 4x² - 6x 

= 2x( 2x - 3 )

b) 9x⁴y³ + 3x²y⁴ 

= 3x²y³( 3x² + y )

c) x³ - 2x² + 5x

= x( x² - 2x + 5 )

d) 3x( x - 1 ) + 5( x - 1 )

= ( x - 1 )( 3x + 5 )

e) 2x²( x + 1 ) + 4( x + 1 )

= ( x + 1 )( 2x² + 4 )

= ( x + 1 )2( x² + 2 )

= 2( x + 1 )( x² + 2 )

f) -3x - 6xy + 9xz

= -( 3x + 6xy - 9xz )

= -3x( 1 + 2y - 3z )

# Học tốt #

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) \(27x^3-54x^2y+36xy^2-8y^3\)

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