Cho x + y = -9. Tính \(D=x^2+2xy+y^2-6x-6y-15\)
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\(D=x^2+2xy+y^2-6x-6y-15\)
\(=\left(x+y\right)^2-6\left(x+y\right)-15=-9^2-6\cdot\left(-9\right)-15=120\)
a) \(6x-6y=6\left(x-y\right)\)
b)\(2xy+3x+6y+xz\)
\(=\left(2xy+xz\right)+\left(6y+3z\right)\)
\(=x\left(2y+z\right)+3\left(2y+z\right)\)
\(=\left(2y+z\right)\left(x+3\right)\)
c)\(x^2+6x+9-y^2\)
\(=\left(x^2+6x+9\right)-y^2\)
\(=\left(x+3\right)^2-y^2\)
\(=\left(x-y+3\right)\left(x+y+3\right)\)
d) \(9x-x^3\)
\(=x\left(9-x^2\right)\)
\(=x\left(3-x\right)\left(3+x\right)\)
e)\(x^2-xy+x-y\)
\(=\left(x^2-xy\right)+\left(x-y\right)\)
\(=x\left(x-y\right)+\left(x-y\right)\)
\(=\left(x-y\right)\left(x+1\right)\)
a, 6x - 6y = 6( x-y )
b, 2xy + 3z + 6y + xz
= ( 2xy + 6y ) + ( 3z + xz )
= 2y( x + 3 ) + z ( 3 + x )
= 2y( 3 + x ) + z ( 3 + x )
= ( 3 + x ) ( 2y + z )
c, x2 + 6x + 9 - y2 = ( x2 + 6x + 9 ) - y2
= ( x + 3 )2 - y2
= ( x + 3 - y ) ( x + 3 + y )
d , 9x - x3 = x ( 9 - x2 )
= x ( 3 - x ) ( 3 + x )
e, x2 - xy + x - y =( x 2 - xy ) + ( x - y )
= x ( x - y ) + ( x - y )
= ( x - y ) ( x + 1 )
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\(D=x^2+2xy+y^2-6x-6y-15\)
\(=\left(x^2+2xy+y^2\right)-\left(6x+6y\right)-15\)
\(=\left(x+y\right)^2-6\left(x+y\right)-15\)
\(=\left(x+y\right)\left(x+y-6\right)-15\)
\(=\left(-9\right)\left(-9-6\right)-15\)
\(=120\)