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a/ \(3x+3y-4x-4y=3\left(x+y\right)-4\left(x+y\right)=\left(x+y\right)\left(3-4\right)=-1\left(x+y\right)\)
b/ \(7x\left(x-y\right)-\left(y-x\right)=7x\left(x-y\right)+\left(x-y\right)=\left(x-y\right)\left(7x+1\right)\)
c/ \(5x\left(1-x\right)+\left(x-1\right)=5x\left(1-x\right)-\left(1-x\right)=\left(1-x\right)\left(5x-1\right)\)
d/ \(4x\left(x-y\right)+3\left(x-y\right)^2=\left(x-y\right)\left(4x+3x-3y\right)=\left(x-y\right)\left(7x-3y\right)\)
e/ \(4x\left(x-y\right)+3\left(y-x\right)^2=4x\left(x-y\right)+3\left(x-y\right)^2=\left(x-y\right)\left(4x+3x-3y\right)=\left(x-y\right)\left(7x-3y\right)\)
g/ \(x^2+8x+7=x^2+x+7x+7=x\left(x+1\right)+7\left(x+1\right)=\left(x+1\right)\left(x+7\right)\)
h/ \(x^2-6x-16=x^2+2x-8x-16=x\left(x+2\right)-8\left(x+2\right)=\left(x+2\right)\left(x-8\right)\)
i/ \(4x^2-8x+3=4x^2-2x-6x+3=2x\left(2x-1\right)-3\left(2x-1\right)=\left(2x-1\right)\left(2x-3\right)\)
k/ \(3x^2-11x+6=3x^2-9x-2x+6=3x\left(x-3\right)-2\left(x-3\right)=\left(x-3\right)\left(3x-2\right)\)
\(x^2+4x-y^2+4\\ =\left(x^2+4x+4\right)-y^2\\ =\left(x+2\right)^2-y^2\\ =\left(x+2-y\right)\cdot\left(x+2+y\right)\)
\(2xy-x^2-y^2+16\\ =\left(x^2-2xy+y^2\right)-16\\ =\left(x-y\right)^2-16\\ =\left(x-y+4\right)\cdot\left(x-y-4\right)\)
\(x^2-2x-4y^2-4y\\ =\left(x^2-4y^2\right)-\left(2x+4y\right)\\ =\left(x-2y\right)\cdot\left(x+2y\right)-2\left(x+2y\right)\\ =\left(x+2y\right)\cdot\left(x-2y+2\right)\)
\(x^2+6x+9-y^2\\ =\left(x-3\right)^2-y^2\\ =\left(x-3-y\right)\cdot\left(x-3+y\right)\)
\(3x^2+6xy+3y^2-3z^2\\ =3\cdot\left(x^2+2xy+y^2-z^2\right)\\ =3\cdot\left[\left(x^2+2xy+y^2\right)-y^2\right]\\ =3\cdot\left[\left(x-y\right)^2-z^2\right]\\ =3\cdot\left(x-y-z\right)\cdot\left(x-y+z\right)\)
\(9x-x^3\\ =x\cdot\left(9-x^2\right)\\ =x\cdot\left(3-x\right)\cdot\left(3+x\right)\)
\(\left(2xy+1\right)^2-\left(2x+y\right)^2\\ =\left(2xy+1-2x-y\right)\cdot\left(2xy+1+2x-y\right)\)
1. x2 - 16 - 4xy + 4y2
= ( x2 - 4xy + 4y2 ) - 16
= ( x - 2y )2 - 42
= ( x - 2y - 4 )( x - 2y + 4 )
2. 4x2 + 4x - 3
= ( 4x2 + 4x + 1 ) - 4
= ( 2x + 1 )2 - 2
= ( 2x + 1 - 2 )( 2x + 1 + 2 )
= ( 2x - 1 )( 2x + 3 )
3. x2 - x - 12
= x2 + 3x - 4x - 12
= x( x + 3 ) - 4( x + 3 )
= ( x + 3 )( x - 4 )
4. 3x + 3y - x2 - 2xy - y2
= ( 3x + 3y ) - ( x2 + 2xy + y2 )
= 3( x + y ) - ( x + y )2
= ( x + y )( 3 - x - y )
5. 4y4 + 16
= 4( y4 + 4 )
= 4( y4 + 4y2 + 4 - 4y2 )
= 4[ ( y4 + 4y2 + 4 ) - 4y2 ]
= 4[ ( y2 + 2 )2 - ( 2y )2 ]
= 4( y2 - 2y + 2 )( y2 + 2y + 2 )
a,\(x^2-16-4xy+4y^2\)
\(=\left(x^2-4xy+4y^2\right)-16\)
\(=\left(x-2y\right)^2-4^2\)
\(=\left(x-2y-4\right)\left(x-2y+4\right)\)
b,\(4x^2+4x-3\)
\(=4x^2-2x+6x-3\)
\(=\left(4x^2-2x\right)+\left(6x-3\right)\)
\(=2x\left(2x-1\right)+3\left(2x-1\right)\)
\(=\left(2x+3\right)\left(2x-1\right)\)
c,\(x^2-x-12\)
\(=x^2-4x+3x-12\)
\(=\left(x^2+3x\right)-\left(4x-12\right)\)
\(=x\left(x+3\right)-4\left(x+3\right)\)
\(=\left(x-4\right)\left(x+3\right)\)
a) \(x^3-2x^2-6x+12\)
\(=x^2\left(x-2\right)-6\left(x-2\right)\)
\(=\left(x-2\right)\left(x^2-6\right)\)
\(=\left(x-2\right)\left(x-\sqrt{6}\right)\left(x+\sqrt{6}\right)\)
b) \(x^4-7x^2+12\)
\(=x^4-3x^2-4x^2+12\)
\(=x^2\left(x^2-3\right)-4\left(x^2-3\right)\)
\(=\left(x^2-3\right)\left(x^2-4\right)\)
\(=\left(x-\sqrt{3}\right)\left(x+\sqrt{3}\right)\left(x-2\right)\left(x+2\right)\)
c) \(x^2-5x+4\)
\(=x^2-x-4x+4\)
\(=x\left(x-1\right)-4\left(x-1\right)\)
\(=\left(x-1\right)\left(x-4\right)\)
d) \(3x^2+5x+2\)
\(=3x^2+3x+2x+2\)
\(=3x\left(x+1\right)+2\left(x+1\right)\)
\(=\left(x+1\right)\left(3x+2\right)\)
e) \(x^3-x+3x^2y+3xy^2+y^3-y\)
\(=\left(x+y\right)^3-\left(x+y\right)\)
\(=\left(x+y\right)\left[\left(x+y\right)^2 -1\right]\)
\(=\left(x+y\right)\left(x^2+y^2+2xy-1\right)\)
a) \(25.\left(x-1\right)^2-16\left(x+y\right)^2\)
= \(\left(5x-5\right)^2-\left(4x+y\right)^2\)
= \(\left(5x-5-4x-y\right)\left(5x-5+4x+y\right)\)
= \(\left(x-y-5\right)\left(9x+y-5\right)\)
b) \(x^3+3x^2+3x+1-27z^3\)
= \(\left(x+1\right)^3-27z^3\)
= \(\left(x+1-3z\right)\left(x^2+x.3z+9z^2\right)\)
c) \(x^2-2xy+y^2-xz+yz\)
= \(\left(x-y\right)^2-z\left(x-y\right)\)
= \(\left(x-y\right)\left(x-y-z\right)\)
d) \(a^3x-ab+b-x\)
= \(x\left(a^3-1\right)-b\left(a-1\right)\)
= \(x\left(a-1\right)\left(a^2+a+1\right)-b\left(a-1\right)\)
= \(\left(a-1\right)\left(a^2x+ax+x-b\right)\)
f) \(x^2+2x-4y^2-4y\)
= \(x^2+2x+1-\left(4y^2+4y+1\right)\)
= \(\left(x+1\right)^2-\left(2y+1\right)^2\)
= \(\left(x+1-2y-1\right)\left(x+1+2y+1\right)\)
= \(\left(x-2y\right)\left(x+2y+2\right)\)
g) \(xy-4+2x-2y\)
= \(y\left(x-2\right)-2\left(x-2\right)\)
= \(\left(x-2\right)\left(y-2\right)\)
a: \(=\left(5x-5\right)^2-\left(4x-4y\right)^2\)
\(=\left(5x-5-4x+4y\right)\cdot\left(5x-5+4x-4y\right)\)
\(=\left(x+4y-5\right)\left(9x-4y-5\right)\)
b: \(=\left(x+1\right)^3-\left(3z\right)^3\)
\(=\left(x+1-3z\right)\left(x^2+2x+1+3xz+3z+9z^2\right)\)
c: \(=\left(x-y\right)^2-z\left(x-y\right)\)
\(=\left(x-y\right)\left(x-y-z\right)\)
d: \(=x\left(a^3-1\right)-b\left(a-1\right)\)
\(=x\left(a-1\right)\cdot\left(a^2+a+1\right)-b\left(a-1\right)\)
\(=\left(a-1\right)\left(a^2x+ax+1-b\right)\)
Ta có
27 x 3 – 64 y 3 = ( 3 x ) 3 – ( 4 y ) 3 = ( 3 x – 4 y ) ( ( 3 x ) 2 + 3 x . 4 y + ( 4 y ) 2 ) = ( 3 x – 4 y ) ( 9 x 2 + 12 x y + 16 )
Vậy đa thức cần điền là 9 x 2 + 12xy + 16
Đáp án cần chọn là: B