\(Q=30^2-29^2+28^2-27^2+...+2^2-1^2\)

\(=\left(30-29\right)\left(30+29\right)+\left(28-27\right)\left(28+27\right)+...+\left(2-1\right)\left(2+1\right)\)

\(=30+29+28+27+...+2+1\)

\(=\frac{30\left(30+1\right)}{2}\)

\(=465\)

xin loi minh ko biet nha bnxin loi minh ko biet nha bn

xin loi minh ko biet nha bn

xin loi minh ko biet nha bn

xin lỗi mình ko bik

xin lỗi minh ko bik

xin lỗi mik kobik

1. Theo mình là sai đề, không biết có phải vậy không

2. (x^2 - 2.x.5 + 25) + (9y^2 - 2.3.2 +4) =0

(x-5)^2 + (3y-2)^2 = 0

TH1: (x-5)^2 = 0

  x-5=0

x=5

TH2:  (3y-2)^2 =0

3y -2=0

y=2/3

1. x²+y²-2x+4y+3=0

<=>(x²-2x+1)+(y²+4y+2)=0

<=>(x-1)²+(y+2)²=0

Mà \(\hept{\begin{cases}\left(x-1\right)^2\ge0\\\left(y+2\right)^2\ge0\end{cases}\Rightarrow\left(x-1\right)^2+\left(y+2\right)^2\ge0}\)

\(\Rightarrow\hept{\begin{cases}\left(x-1\right)^2=0\\\left(y+2\right)^2=0\end{cases}\Rightarrow\hept{\begin{cases}x=1\\y=-2\end{cases}}}\)

a)(ab−1)2+(a+b)2

=a2b2−2ab+1+a2+2ab+b2

=a2b2+1+a2+b2=a2(b2+1)+(b2+1) = (a2+1)(b2+1)

c)x3−4x2+12x−27

=x3−27+(−4x2+12x)

=(x−3)(x2+3x+9)−4x(x−3)

=(x−3)(x2+3x+9−4x)

=(x−3)(x2−x+9)

b)x3+2x2+2x+1

=x3+2x2+x+x+1

=x(x2+2x+1)+(x+1)

=x(x+1)2+(x+1)

=(x+1)(x(x+1)+1)

=(x+1)(x2+x+1)

d)x4−2x3+2x−1

=x4−2x3+x2−x2+2x−1

=x2(x2−2x+1)−(x2−2x+1)

=(x2−2x+1)(x2−1)

=(x−1)2(x−1)(x+1)

=(x−1)3(x+1)

e)x4+2x3+2x2+2x+1

=x4+2x3+x2+x2+2x+1

=x2(x2+2x+1)+(x2+2x+1)

=(x2+2x+1)(x2+1)

=(x+1)2(x2+1)

1. ( 2x + y )( 4x² - 2xy + y² ) - 8x³ - y³ - 16

= [ ( 2x )³ + y³ ] - 8x³ - y³ - 16

= 8x³ + y³ - 8x³ - y³ - 16

= -16 ( đpcm )

2. ( 3x + 2y )² + ( 3x + 2y )² - 18x² - 8y² + 3

= 2( 3x + 2y )² - 18x² - 8y² + 3

= 2( 9x² + 12xy + 4y² ) - 18x² - 8y² + 3

= 18x² + 24xy + 8y² - 18x² - 8y² + 3

= 24xy + 3 ( có phụ thuộc vào biến )

3. ( -x - 3 )³ + ( x + 9 )( x² + 27 ) + 19

= -x³ - 9x² - 27x - 27 + x³ + 9x² + 27x + 243 + 19

= -27 + 243 + 19 = 235 ( đpcm )

4. ( x - 2 )³ - x( x + 1 )( x - 1 ) + 13( x - 4 )

= x³ - 6x² + 12x - 8 - x( x² - 1 ) + 13x - 52

= x³ - 6x² + 12x - 8 - x³ + x + 13x - 52

= -6x² + 26x - 60 ( có phụ thuộc vào biến )

1. (2x+y).(4x²-2xy+y²)-8x³-y³-16

=(2x)³+y³-8x³-y³-16

=-16

Vậy đa thức trên kh phụ thuộc vào biến x

2. (3x+2y)²+(3x+2y)²-18x²-8y²+3

=(9x²+12xy+4y²)+(9x²+12xy+4y²)-18x²-8y²+3

=9x²+12xy+4y²+9x²+12xy+4y²-18x²-8y²+3

=24xy+3

Vậy đa thức trên phụ thuộc biến x

a)\(=>x^3+9x^2+27x+27-9x^3-6x^2-x+8x^3+1=28\)

\(=>3x^2+26x=0\)

\(=>x\left(3x+26\right)=0\)

Đến đây tự tìm nha

Câu b thế câu a vào xong khử bớt đi là ra

a) ( 3x - 1 )² - 16 = ( 3x - 1 )² - 4² = ( 3x - 1 - 4 )( 3x - 1 + 4 ) = ( 3x - 5 )( 3x + 3 ) = 3( 3x - 5 )( x + 1 )

b) ( 5x - 4 )² - 49x² = ( 5x - 4 )² - ( 7x )² = ( 5x - 4 - 7x )( 5x - 4 + 7x ) = ( -2x - 4 )( 12x - 4 ) = -2( x + 2 ).4( 3x - 1 ) = -8( x + 2 )( 3x - 1 )

c) ( 2x + 5 )² - ( x - 9 )² = [ ( 2x + 5 ) - ( x - 9 ) ][ ( 2x + 5 ) + ( x - 9 ) ] = ( 2x + 5 - x + 9 )( 2x + 5 + x - 9 ) = ( x + 14 )( 3x - 4 )

d) ( 3x + 1 )² - 4( x - 2 )² = ( 3x + 1 )² - 2²( x - 2 )² = ( 3x + 1 )² - [ 2( x - 2 ) ]² = ( 3x + 1 )² - ( 2x - 4 )² = [ ( 3x + 1 ) - ( 2x - 4 ) ][ ( 3x + 1 ) + ( 2x - 4 ) ] = ( 3x + 1 - 2x + 4 )( 3x + 1 + 2x - 4 ) = ( x + 5 )( 5x - 3 )

e) 9( 2x + 3 )² - 4( x + 1 )² = 3²( 2x + 3 )² - 2²( x + 1 )² = [ 3( 2x + 3 ) ]² - [ 2( x + 1 ) ]² = ( 6x + 9 )² - ( 2x + 2 )² = [ ( 6x + 9 ) - ( 2x + 2 ) ][ ( 6x + 9 ) + ( 2x + 2 ) ] = ( 6x + 9 - 2x - 2 )( 6x + 9 + 2x + 2 ) = ( 4x + 7 )( 8x + 11 )

f) 4b²c² - ( b² + c² - a² )² = ( 2bc )² - ( b² + c² - a² )² = [ 2bc - ( b² + c² - a² ) ][ 2bc + ( b² + c² - a² ] = ( 2bc - b² - c² + a² )( 2bc + b²+ c² - a² ) = [ a² - ( b² - 2bc + c² ) ][ ( b² + 2bc + c² ) - a² ] = [ a² - ( b - c )² ][ ( b + c )² - a² ] = ( a - b + c )( a + b - c )( b + c - a )( b + c + a )

g) ( ax + by )² - ( ay + bx )² 

= [ ( ax + by ) - ( ay + bx ) ][ ( ax + by ) + ( ay + bx ) ]

= ( ax + by - ay - bx )( ax + by + ay + bx )

= [ a( x - y ) - b( x - y ) ][ a( x + y ) + b( x + y ) ]

= ( a - b )( x - y )( x + y )( a + b )

h) ( a² + b² - 5 )² - 4( ab + 2 )² 

= ( a² + b² - 5 )² - 2²( ab + 2 )² 

= ( a² + b² - 5 )² - [ 2( ab + 2 ) ]² 

= ( a² + b² - 5 )² - ( 2ab + 4 )² 

= [ ( a² + b² - 5 ) - ( 2ab + 4 ) ][ ( a² + b² - 5 ) + ( 2ab + 4 ) ]

= ( a² + b² - 5 - 2ab - 4 )( a² + b² - 5 + 2ab + 4 )

= [ ( a² - 2ab + b² ) - 9 ][ ( a² + 2ab + b² ) - 1 ]

= [ ( a - b )² - 3² ][ ( a + b )² - 1² ]

= ( a - b - 3 )( a - b + 3 )( a + b - 1 )( a + b + 1 )

i) ( 4x² - 3x - 18 )² - ( 4x² + 3x )²

= [ ( 4x² - 3x - 18 ) - ( 4x² + 3x ) ][ ( 4x² - 3x - 18 ) + ( 4x² + 3x ) ]

= ( 4x² - 3x - 18 - 4x² - 3x )( 4x² - 3x - 18 + 4x² + 3x )

= ( -6x - 18 )( 8x² - 18 )

= -6( x + 3 ).2( 4x² - 9 )

= -12( x + 3 )( 2x - 3 )( 2x + 3 )

k) 9( x + y - 1 )² - 4( 2x + 3y + 1 )²

= 3²( x + y - 1 )² - 2²( 2x + 3y + 1 )²

= [ 3( x + y - 1 ) ]² - [ 2( 2x + 3y + 1 ) ]²

= ( 3x + 3y - 3 )² - ( 4x + 6y + 2 )²

= [ ( 3x + 3y - 3 ) - ( 4x + 6y + 2 ) ][ ( 3x + 3y - 3 ) + ( 4x + 6y + 2 ) ]

= ( 3x + 3y - 3 - 4x - 6y - 2 )( 3x + 3y - 3 + 4x + 6y + 2 )

= ( -x - 3y - 5 )( 7x + 9y - 1 )

l) -4x² + 12xy - 9y² + 25

= 25 - ( 4x² - 12xy + 9y² )

= 5² - ( 2x - 3y )²

= ( 5 - 2x + 3y )( 5 + 2x - 3y )

m) x² - 2xy + y² - 4m² + 4mn - n²

= ( x² - 2xy + y² ) - ( 4m² - 4mn + n² )

= ( x - y )² - ( 2m - n )²

= ( x - y - 2m + n )( x - y + 2m - n )

\(a,x^3+9x^2+27x+27-27z^3\)

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

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

.........

\(b,\)

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

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

\(c,\)

\(=x^2\left(x^2+10\right)-2x\left(x^2+10\right)\)

\(=x\left(x-2\right)\left(x+10\right)\)