B1 : a, M = x³-3xy(x-y)-y³-x²+2xy-y²

= ( x³-y³)-3xy(x-y) -(x²-2xy+y²)

= (x-y)(x²+xy+y²)-3xy(x-y)-(x-y)²

= (x-y) [(x²+xy+y²-3xy-(x-y)]

= (x-y)[(x²-2xy+y²)-(x-y)

= (x-y)[(x-y)²-(x-y)]

= (x-y)(x-y)(x-y-1)

= (x-y)²(x-y-1)

= 7²(7-1) = 49 . 6= 294

N = x²(x+1)-y²(y-1)+xy-3xy(x-y+1)-95

= x³+x²-(y³-y²)+xy-(3x²y-3xy²+3xy)-95

= x³+x²-y³+y²+xy-3x²y+3xy²-3xy-95

= (x³-y³)+(x²-2xy+y²)-(3x²y+y²)-(3x²y-3xy²)-95

=(x-y)(x²+xy+y²)+(x-y)²-3xy(x-y)-95

= (x-y)(x²+xy+y²+x-y-3xy)-95

= (x-y)[(x²-2xy+y²)+(x-y)]-95

= (x-y)[(x-y)²+(x-y)]-95

=(x-y)(x-y)(x-y+1)-95

= (x-y)²(x-y+1)-95

= 7²(7+1)-95=297

16y^2+2yz+40y+5z=

a: \(M=6x^2+9xy-y^2-5x^2+2xy=x^2+11xy-y^2\)

b: \(N=3xy-4y^2-x^2+7xy-8y^2=-x^2+10xy-12y^2\)

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

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

Dấu '=' xảy ra khi x=-1

2: \(=-\left(4x^2-12x-10\right)\)

\(=-\left(4x^2-12x+9-19\right)\)

\(=-\left(2x-3\right)^2+19< =19\)

Dấu '=' xảy ra khi x=3/2

3: \(=-\left(x^2+4x+4-4\right)=-\left(x+2\right)^2+4< =4\)

Dấu '=' xảy ra khi x=-2

Bài 1 :

a) \(3x\left(5x^2-2x-1\right)=3x\cdot5x^2+3x\left(-2x\right)+3x\left(-1\right)\)

\(=15x^3-6x^2-3x\)

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

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

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

c) \(\frac{1}{2}x^2y\left(2x^3-\frac{2}{5}xy-1\right)\)

\(=\frac{1}{2}x^2y\cdot2x^3+\frac{1}{2}x^2y\cdot\left(-\frac{2}{5}xy\right)+\frac{1}{2}x^2y\left(-1\right)\)

\(=x^5y-\frac{1}{5}x^3y^2-\frac{1}{2}x^2y\)

d) \(\frac{1}{2}xy\left(\frac{2}{3}x^2-\frac{3}{4}xy+\frac{4}{5}y^2\right)\)

\(=\frac{1}{2}xy\cdot\frac{2}{3}x^2+\frac{1}{2}xy\cdot\left(-\frac{3}{4}xy\right)+\frac{1}{2}xy\cdot\frac{4}{5}y^2\)

\(=\frac{1}{3}x^3y-\frac{3}{8}x^2y^2+\frac{2}{5}xy^3\)

e) \(\left(x^2y-xy+xy^2+y^3\right)\left(3xy^3\right)\)

= \(x^2y\cdot3xy^3-xy\cdot3xy^3+xy^2\cdot3xy^3+y^3\cdot3xy^3\)

\(=3x^3y^4-3x^2y^4+3x^2y^5+3xy^6\)

Bài 2 :

3(2x - 1) + 3(5 - x) = 6x - 3 + 15 - x = (6x - x) - 3 + 15 = 5x - 3 + 15

Thay x = -3/2 vào biểu thức trên ta có : \(5\cdot\left(-\frac{3}{2}\right)-3+15\)

\(=-\frac{15}{2}-3+15=\frac{9}{2}\)

b) 25x - 4(3x - 1) + 7(5 - 2x)

= 25x - 12x + 4  + 35 - 14x

= (25x - 12x - 14x) + 4 + 35 = -x + 4 + 35 = -x + 39

Thay \(x=2\)vào biểu thức trên ta có : -2 + 39 = 37

c) 4x - 2(10x + 1) + 8(x - 2)

= 4x - 20x - 2 + 8x - 16

= (4x - 20x + 8x) - 2 - 16 = -8x - 2 - 16 = -8x - 18

Thay x = 1/2 vào biểu thức trên ta có \(-8\cdot\frac{1}{2}-18=-4-18=-22\)

d) Tương tự

Bài 3:

a) \(2x\left(x-4\right)-x\left(2x+3\right)=4\)

=> 2x² - 8x - 2x² - 3x = 4

=> (2x² - 2x²) + (-8x - 3x) = 4

=> -11x = 4

=> x = \(-\frac{4}{11}\)

b) x(5 - 2x) + 2x(x - 7) = 18

=> 5x - 2x² + 2x² - 14x = 18

=> 5x - 14x = 18

=> -9x = 18

=> x = -2

Còn 2 câu làm tương tự

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