\(\left(x^2+3x+1\right)\left(x^2+3x+2\right)-6\)

Đặt \(\left(x^2+3x+1\right)=a\), ta được:

\(a\left(a+1\right)-6\)\(=a^2+a-6\)\(=\left(a^2+3a\right)-\left(2a+6\right)\)\(=a\left(a+3\right)-2\left(a+3\right)\)

\(=\left(a+3\right)\left(a-2\right)\)

Thay \(a=\left(x^2+3x+1\right)\), ta được:

\(=\left(x^2+3x+1+3\right)\left(x^2+3x+1-2\right)\)

\(=\left(x^2+3x+4\right)\left(x^2+3x-1\right)\)

\(\left(x^2+3x+1\right)\left(x^2+3x+2\right)-6\)

Đặt \(x^2+3x+1=a,\)ta được:

\(a\left(a+1\right)-6\)

\(=a^2+a-6=\left(a^2+3a\right)-\left(2a+6\right)\)

\(=a\left(a+3\right)-2\left(a+3\right)=\left(a+3\right)\left(a-2\right)\)

Thay \(a=x^2+3x+1,\)ta được:

\(\left(x^2+3x+1+3\right)\left(x^2+3x+1-2\right)\)\(=\left(x^2+3x+4\right)\left(x^2+3x-1\right)\)

a: \(2y\left(x+2\right)-3x-6\)

\(=2y\left(x+2\right)-3\left(x+2\right)\)

\(=\left(x+2\right)\left(2y-3\right)\)

b: \(3\left(x+4\right)-x^2-4x\)

\(=3\left(x+4\right)-\left(x^2+4x\right)\)

\(=3\left(x+4\right)-x\left(x+4\right)\)

\(=\left(x+4\right)\left(3-x\right)\)

c: \(2\left(x+5\right)-x^2-4x\)

\(=2x+10-x^2-4x\)

\(=-x^2-2x+10\)

\(=-x^2-2x-1+11\)

\(=11-\left(x^2+2x+1\right)\)

\(=11-\left(x+1\right)^2\)

\(=\left(\sqrt{11}-x-1\right)\left(\sqrt{11}+x+1\right)\)

d: \(x^2+6x-3x-18\)

\(=\left(x^2+6x\right)-\left(3x+18\right)\)

\(=x\left(x+6\right)-3\left(x+6\right)\)

\(=\left(x+6\right)\left(x-3\right)\)

( x + 2 ) ( x² - 2x ) - 3x - 6

= ( x + 2 ) ( x² - 2x ) - ( 3x + 6 )

= ( x + 2 ) ( x² - 2x ) - 3 ( x + 2 )

= ( x + 2 ) ( x² - 2x - 3 )

= ( x + 2 ) [ ( x² + x ) - ( 3x + 3 ) ]

= ( x + 2 ) [ x ( x + 1 ) - 3 ( x + 1 ) ]

= ( x + 2 ) ( x - 3 ) ( x + 1 ) 

( x + 2 )( x² - 2x ) - 3x - 6

= ( x + 2 )( x² - 2x ) - 3( x + 2 )

= ( x + 2 )( x² - 2x - 3 )

= ( x + 2 )[ ( x² - 2x + 1 ) - 4 ]

= ( x + 2 )[ ( x - 1 )² - 2² ]

= ( x + 2 )( x - 1 - 2 )( x - 1 + 2 )

= ( x + 2 )( x - 3 )( x + 1 )

\(\left(x+3\right)^2-\left(2x+6\right)\left(1-3x\right)+\left(3x+1\right)^2\)

\(=x^2+6x+9-\left(2x-6x^2+6-18x\right)+9x^2+6x+1\)

\(=10x^2+12x+10+6x^2+16x-6=16x^2+28x+4\)

\(=4\left(4x^2+7x+1\right)\)

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