\(A=9y^2+12x^2-6xy+12y-6x+200\)

Rút gọn A ta có:

\(A=y\left(9y-12\right)+x\left(12x-6-6y\right)+200\)

\(MinA=0\Leftrightarrow y\left(9y-12\right)+x\left(12x-6-6y\right)=-200\)

Trả lời:

7, 5( x + y )² + 15( x + y )

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

9, 7x( y - 4 )² - ( 4 - y )³ 

= 7x ( 4 - y )² - ( 4 - y )

= ( 4 - y )² ( 7x - 4 + y )

11, ( x + 1 )( y - 2 ) - ( 2 - y )²

= ( x + 1 )( y - 2 ) - ( y - 2 )²

= ( y - 2 )( x + 1 - y + 2 )

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

8, 9x ( x - y ) - 10 ( y - x )² 

= 9x ( x - y ) - 10 ( x - y )²

= ( x - y )[ ( 9x - 10 ( x - y ) ]

= ( x - y )( 9x - 10x + 10y )

= ( x - y )( 10y - x )

10, ( a - b )² - ( a + b )( b - a ) 

= ( b - a )² - ( a + b )( b - a )

= ( b - a )( b - a - a - b )

= - 2a( b - a )

= 2a ( a - b )

12, 2x ( x - 3 ) + y ( x - 3 ) + ( 3 - x )

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

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

a. \(-4x^2-4x-2\)

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

\(=-\left[\left(2x\right)^2+2.2x+1+1\right]\)

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

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

vì \(\left(2x+1\right)^2\ge0\forall x\Rightarrow-\left(2x+1\right)^2\le0\forall x\)

\(\Rightarrow-\left(2x+1\right)^2-1\le-1\forall x\)hay \(-4x^2-4x-2< 0\)

b. \(x^2+x+1\)

\(=x^2+2.\frac{1}{2}x+\left(\frac{1}{2}\right)^2+\frac{3}{4}\)

\(=\left(x+\frac{1}{2}\right)^2+\frac{3}{4}>0\)

chúc bạn học tốt, k đúng cho mình nha, cảm ơn b

a)

\(x^2+6x+9\)

\(\Leftrightarrow\left(x+3\right)^2\)

b) \(\frac{1}{4}x^2-\frac{1}{2}x+1\)

\(\Leftrightarrow\left(\frac{1}{2}-x\right)^2\)

#Cừu

\(\left(ab+cd\right)^2=\left(ab\right)^2+\left(cd\right)^2=a^2b^2c^2d^2=ab.ab+cd.cd\ge k\)abcd

\(\Leftrightarrow Max\)\(k=15\)

phân tích đa thức thành nhân tử hả bạn ?

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

b, \(x^2-4x+4-y^2=\left(x-2\right)^2-y^2=\left(x-2-y\right)\left(x-2+y\right)\)

đề bài là gì vậy bạn

a) = ( x - 3 )² - ( 3x )² = ( -2x - 3 )( 4x - 3 )

b) = x( x - 2y ) - ( x - 2y ) = ( x - 2y )( x - 1 )

a) \(\left(x-3-3x\right).\left(x-3+3x\right)\)

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

a) = x⁴ + 4x² + 4 - 4x² = ( x² + 2 )² - ( 2x )² = ( x² - 2x + 2 )( x² + 2x + 2 )

b) = 64x⁴ + 16x² + 1 - 16x² = ( 8x² + 1 )² - ( 4x )² = ( 8x² - 4x + 1 )( 8x² + 4x + 1 )

c) = 81x⁴ + 36x² + 4 - 36x² = ( 9x² + 2 )² - ( 6x )² = ( 9x² - 6x + 2 )( 9x² + 6x + 2 )

d) bạn xem lại đề

c) = ( x - 2 )² - y² = ( x - y - 2 )( x + y - 2 )