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1
a, 2x2+4x+2-2y2 = 2(x2+2x+1-y2)= 2[(x+1)2-y2 ] = 2(x-y+1)(x+y+1)
b, 2x - 2y - x2 + 2xy - y2= 2(x -y) - (x2 - 2xy + y2) = 2(x-y)-(x-y)2=(x-y)(2-x+y)
c, x2-y2-2y-1=x2-(y2+2y+1)=x2-(y+1)2=(x-y-1)(x+y+1)
d, x2-4x-2xy-4y+y2= x2-2xy+y2-4x-4y=(x-y)
2.
a, x2-3x+2=x2-x-2x+2=x(x-1)-2(x-1)=(x-2)(x-1)
b, x2+5x+6=x2+2x+3x+6=x(x+2)+3(x+2)=(x+3)(x+2)
c, x2+6x-6=
\(x^2-25+y^2+2xy\)
\(=\left(x^2+2xy+y^2\right)-25\)
\(=\left(x+y\right)^2-5^2\)
\(=\left(x+y-5\right)\left(x+y+5\right)\)
1) x^2-4x^2y^2+y^2+2xy
=x2+2xy+y2-4x2y2
=(x+y)2-4x2y2
=(x+2xy+y)(x-2xy+y)
2) 25-a^2+2ab-b^2
=25-(a2-2ab+b2)
=25-(a-b)2
=[5-(a-b)][5+(a-b)]
=(5-a+b)(5+a-b)
Bài 1:
\(=3x^3y-6x^2y^2+15xy\)
Bài 2:
\(=\left(x+y\right)^2-25=\left(x+y+5\right)\left(x+y-5\right)\)
\(x^2+2xy-25+y^2\\ =\left(x^2+2xy+y^2\right)-5^2\\ =\left(x+y\right)^2-5^2\\ =\left(x+y-5\right)\left(x+y+5\right)\)
a) x3-2x2-x+2
=x(x2-1)+2(-x2+1)
=x(x2-1)-2(x2-1)
=(x2-1)(x-2)
b)
x2+6x-y2+9
=x2+6x+9-y2
=(x+3)2-y2
=(x+3-y)(x+3+y)
a) \(2x^2-2y^2=2\left(x^2-y^2\right)=2\left(x-y\right)\left(x+y\right)\)
b) \(x^2+2x+1-y^2=\left(x+1\right)^2-y^2=\left(x+y+1\right)\left(x-y+1\right)\)
c) \(x^2-4x=x\left(x-4\right)\)
d) \(x^2+10x+25=x^2+2.5x+5^2=\left(x+5\right)^2\)
e) \(x^2-2xy+y^2-9=\left(x-y\right)^2-3^2=\left(x-y+3\right)\left(x-y-3\right)\)
\(2x^2-2y^2=2.\left(x^2-y^2\right)=2.\left(x-y\right)\left(x+y\right)\)
\(x^2+2x+1-y^2=\left(x+1\right)^2-y^2=\left(x+1-y\right)\left(x+1+y\right)\)
\(x^2-4x=x.\left(x-4\right)\)
\(x^2+10x+25=x^2+2.x.5+5^2=\left(x+5\right)^2\)
\(x^2-2xy+y^2-9=\left(x-y\right)^2-3^2=\left(x-y-3\right)\left(x-y+3\right)\)
Tham khảo nhé~
a) \(3x^2-6xy+3y^2-12z^2\)
\(=3\left(x^2-2xy+y^2-4z^2\right)\)
\(=3\left[\left(x-y\right)^2-\left(2z\right)^2\right]\)
\(=3\left(x-y-2z\right)\left(x-y+2z\right)\)
b) \(x^2-25+y^2+2xy\)
\(=\left(x^2+2xy+y^2\right)-25\)
\(=\left(x+y\right)^2-5^2\)
\(=\left(x+y+5\right)\left(x+y-5\right)\)
Bài 3. a) x(x-2)-2x+x=0
<=> x2-2x-2x+x=0
<=>x2-4x+x=0
<=>x2-3x=0
<=> x(x-3)=0 => x=0; x=3.
`#040911`
`a)`
`x^2 + y^2 + 2xy - 25`
`= (x^2 + 2xy + y^2) - 25`
`= [ (x)^2 + 2*x*y + (y)^2] - 5^2`
`= (x + y)^2 - 5^2`
`= (x + y - 5)(x + y + 5)`
`b)`
`x^2 + 2x - 15`
`= x^2 + 5x - 3x - 15`
`= (x^2 + 5x) - (3x + 15)`
`= x(x + 5) - 3(x + 5)`
`= (x - 3)(x + 5)`
`c)`
`x^2 - x - 2`
`= x^2 - 2x + x - 2`
`= (x^2 - 2x) + (x - 2)`
`= x(x - 2) + (x - 2)`
`= (x + 1)(x - 2)`
`d)`
`3x^2 - 11x + 6`
`= 3x^2 - 9x - 2x + 6`
`= (3x^2 - 9x) - (2x - 6)`
`= 3x(x - 3) - 2(x - 3)`
`= (3x - 2)(x - 3)`
`a, (x+y)^2-25 = (x+y+5)(x+y-5)`.
`b, x^2+2x-15 = (x+1)^2-16 = (x-3)(x+5)`.
`c, x^2-x-2=(x-2)(x+1)`
`d, 3x^2-11x+6 = (3x-2)(x-3)`.
a) 752 - 252 = ( 75 - 25 )( 75 + 25 ) = 50.100 = 5000
b) x2 + 2xy + y2 - 9z2
= ( x2 + 2xy + y2 ) - 9z2
= ( x + y )2 - ( 3z )2
= ( x + y - 3z )( x + y + 3z )