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\(2x^2+6x-4\left(x+3\right)\)
\(=\left(2x^2+6x\right)-4\left(x+3\right)\)
\(=2x\left(x+3\right)-4\left(x+3\right)\)
\(=\left(x+3\right)\left(2x+4\right)\)
\(=2\left(x+3\right)\left(x+2\right)\)
______
\(xy\left(x-y\right)-5x+5y\)
\(=xy\left(x-y\right)-\left(5x-5y\right)\)
\(=xy\left(x-y\right)-5\left(x-y\right)\)
\(=\left(x-y\right)\left(xy-5\right)\)
______
\(2x^2+3x-4xy-6y\)
\(=\left(2x^2+3x\right)-\left(4xy+6y\right)\)
\(=x\left(2x+3\right)-2y\left(2x+3\right)\)
\(=\left(x-2y\right)\left(2x+3\right)\)
2x² + 6x - 4(x + 3)
= (2x² + 6x) - 4(x + 3)
= 2x(x + 3) - 4(x + 3)
= (x + 3)(2x - 4)
= 2(x + 3)(x - 2)
------------
xy(x - y) - 5x + 5y
= xy(x - y) - (5x - 5y)
= xy(x - y) - 5(x - y)
= (x - y)(xy - 5)
------------
2x² + 3x - 4xy - 6y
= (2x² - 4xy) + (3x - 6y)
= 2x(x - 2y) + 3(x - 2y)
= (x - 2y)(2x + 3)
\(x^3+y^3+z^3-3xyz=\left(x+y\right)^3+z^3-3xy\left(x+y\right)-3xyz=\left(x+y+z\right)\left[\left(x+y\right)^2-z\left(x+y\right)+z^2\right]-3xy\left(x+y+z\right)=\left(x+y+z\right)\left(x^2+2xy+y^2-xz-yz+z^2-3xy\right)=\left(x+y+z\right)\left(x^2+y^2+z^2-xy-yz-xz\right)\)
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
\(2x^3+5x^2-2x+a=x\left(2x^2-x+1\right)+3\left(2x^2-x+1\right)-3+a\)
\(=\left(2x^2-x+1\right)\left(x+3\right)-3+a⋮\left(2x^2-x+1\right)\)
\(\Rightarrow-3+a=0\Rightarrow a=3\)
\(2x^3+5x^2-2x+a⋮2x^2-x+1\)
\(\Leftrightarrow2x^3-x^2+x+6x^2-3x+3+a-3⋮2x^2-x+1\)
\(\Leftrightarrow a-3=0\)
hay a=3
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( 2x2 - y )3 - 64y3
= ( 2x2 - y )3 - ( 4y )3
= ( 2x2 - y - 4y )[ ( 2x2 - y )2 + ( 2x2 - y ).4y + ( 4y )2 ]
= ( 2x2 - 5y )( 4x4 - 4x2y + y2 + 8x2y - 4y2 + 16y2 )
= ( 2x2 - 5y )( 4x4 + 4x2y + 13y2 )