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a, \(9x^2+6xy+y^2=\left(3x\right)^2+2\times3xy+y^2=\left(3x+y\right)^2\)
b, \(6x-9-x^2=-\left(x^2-2\times3x+3^2\right)=-\left(x-3\right)^2\)
c, \(x^2+4y^2+4xy=x^2+2\times2xy+\left(2y\right)^2=\left(x+2y\right)^2\)
\(x^2-y^2+6x+9=\left(x+3\right)^2-y^2=\left(x+3+y\right)\left(x+3-y\right)\)
\(x^3+3x^2-9x-27=\left(x-3\right)\left(x^2+3x+9\right)+3x\left(x-3\right)=\left(x-3\right)\left(x^2+6x+9\right)=\left(x-3\right)\left(x+3\right)^2\)
- 3x2 + (x2 - 6x + 9)
= (x - 3)2 - 3x2 = (x - 3 - \(\sqrt{3}x\))(x - 3 + \(\sqrt{3}x\))
Ta có: \(3x^2\left(y-x\right)+6x^2\left(x-y\right)^2\)
\(=3x^2\left(y-x\right)+6x^2\left(y-x\right)^2\)
\(=3x^2\left(y-x\right)\left[1-2\left(y-x\right)\right]\)
\(=3x^2\left(y-x\right)\left(2x-2y+1\right)\)
3x2( y - x ) + 6x2( x - y )2
= 3x2( y - x ) + 6x2( y - x )2
= 3x2( y - x )[ 1 + 2( y - x ) ]
= 3x2( y - x )( 2y - 2x + 1 )
\(49-x^2+6x-9\)
\(=7^2-\left(x^2+2.x.3+3^2\right)\)
\(=7^2-\left(x+3\right)^2\)
\(=\left(7-x-3\right)\left(7+x+3\right)\)
\(=\left(4-x\right)\left(10+x\right)\)
x2 + 6x - y2 + 9 =
= ( x2 + 6x + 9 ) - y2
= ( x + 3 )2 - y2
= ( x + 3 - y ) . ( x + 3 + y )
Hok tốt!!!!!!!!!!!
b) \(9x^3+6x^2+x\)
\(=x\left(9x^2+6x+1\right)\)
\(=x\left(3x+1\right)^2\)
c) \(x^4+5x^3+15x-9\)
\(=\left(x^4-9\right)+5x\left(x^2+3\right)\)
\(=\left(x^2-3\right)\left(x^2+3\right)+5x\left(x^2+3\right)\)
\(=\left(x^2+3\right)\left(x^2-3+5x\right)\)
a) \(x^2-y^2+10y-25\)
\(=x^2-\left(y^2-10y+25\right)\)
\(=x^2-\left(y-5\right)^2\)
\(=\left(x-y+5\right)\left(x+y-5\right)\)
a) (x2-6x+9)-y2=(x-3)2-y2=(x-3-y)(x-3+y)