Bài 1: 

a) Ta có: \(\left(15x^2\cdot y^2\cdot z\right):3xyz\)

\(=\dfrac{15x^2y^2z}{3xyz}\)

\(=5xy\)

b) Ta có: \(3x^2\cdot\left(5x^2-4x+3\right)\)

\(=3x^2\cdot5x^2-3x^2\cdot4x+3x^2\cdot3\)

\(=15x^4-12x^3+9x^2\)

c) Ta có: \(\left(2x^2-3x\right):\left(x-4\right)\)

\(=\dfrac{2x^2-8x+5x-20+20}{x-4}\)

\(=\dfrac{2x\left(x-4\right)+5\left(x-4\right)+20}{x-4}\)

\(=2x+5+\dfrac{20}{x-4}\)

d) Ta có: \(-5xy\cdot\left(3x^2y-5xy+y^2\right)\)

\(=-5xy\cdot3x^2y+5xy\cdot5xy-5xy\cdot y^2\)

\(=-15x^3y^2+25x^2y^2-5xy^3\)

a: \(A=\dfrac{2}{3}x^2y\cdot\dfrac{3}{4}x^4y^3=\dfrac{1}{2}x^6y^4\)

\(B=\dfrac{-1}{2}xy^2\cdot4x^5y^2=-2x^6y^4\)

b: \(C=A-B=\dfrac{-3}{2}x^6y^4\)

Bậc là 10

c: A-B nhận được giá trị âm với mọi x,y

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

f) = x²( x - 4 ) - 9( x - 4 ) = ( x - 4 )( x - 3 )( x + 3 )

g) = 4( x - y ) + ( x - y )² = ( x - y )( x - y + 4 )

h) = x³( x + 1 ) + ( x - 1 )( x + 1 ) = ( x + 1 )( x³ + x - 1 )

i) = ( x - y )( x + y ) - 4( x + y ) = ( x + y )( x - y - 4 )

j) = ( x - y )( x² + xy + y² ) - 3( x - y ) = ( x - y )( x² + xy + y² - 3 )

Trả lời:

f, x³ - 4x² - 9x + 36 = ( x³ - 4x² ) - ( 9x - 36 ) = x² ( x - 4 ) - 9 ( x - 4 ) = ( x - 4 )( x² - 9 ) = ( x - 4 )( x - 3 )( x + 3 )

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

h, x⁴ + x³ + x² - 1 = ( x⁴ + x³ ) + ( x² - 1 ) =  x³ ( x + 1 ) + ( x - 1 )( x + 1 ) = ( x + 1 )( x³ + x - 1 ) 

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

j, x³ - y³ - 3x + 3y = ( x³ - y³ ) - ( 3x - 3y ) = ( x - y )( x² + xy + y² ) - 3 ( x - y ) = ( x - y )( x² + xy + y² - 3 ) 

f) x³-4x²-9x+36

=x²(x-4)-9(x-4)

=(x-4)(x²-9)

=(x-4)(x-3)(x+3)

g) 4x-4y+x²-2xy+y²

=4(x-y)+(x-y)²

=(x-y)(4+x-y)

h) x⁴+x³+x²-1

=x³(x+1)+(x-1)(x+1)

=(x+1)(x³+x-1)

i) x²-y²-4x-4y

=(x-y)(x+y)-4(x+y)

=(x+y)(x-y-4)

j) x³-y³-3x+3y

=(x-y)(x²+xy+y²)-3(x-y)

=(x-y)(x²+xy+y²-3)

#H