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`Answer:`
`a)`
`A=5(x+1)^2-3(x-3)^2-4(x^2-4)`
`=>A=5(x^2+2x+1)-3(x^2-6x+9)-4x^2+16`
`=>A=5x^2+10x+5-3x^2+18x-27-4x^2+16`
`=>A=(5x^2-3x^2-4x^2)+(10x+18x)+(5-27+16)`
`=>A=-2x^2+28x-6`
`b)`
`B=5(x+1)^2-3(x-3)^2-4(x+2)(x-2)`
`=2x(3x+5)-3(3x+5)-2x(x^2-4x+4)-[(2x)^2-3^2]`
`=6x^2+10x-9x-15-2x^3+8x^2-8x-4x^2+9`
`=(6x^2-4x^2+8x^2)-2x^3+(10x-9x-8x)+(-15+9)`
Thay `x=-7` vào ta được:
`B=10(-7)^2-2(-7)^3-7(-7)-6`
`=>B=10.49-2(-343)+49-6`
`=>B=490+686+49-6`
`=>B=1219`
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{x^3+x^2+x+1}{3x^2+6x+3}=\frac{x^2\left(x+1\right)+\left(x+1\right)}{3x^2+3x+3x+3}\)
\(=\frac{\left(x^2+1\right)\left(x+1\right)}{3x\left(x+1\right)+3\left(x+1\right)}=\frac{\left(x^2+1\right)\left(x+1\right)}{\left(3x+3\right)\left(x+1\right)}\)
\(=\frac{\left(x^2+1\right)\left(x+1\right)}{3\left(x+1\right)^2}=\frac{x^2+1}{3\left(x+1\right)}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
(x+1)^3-(x-1)^3-6(x+1)^2=x^3+3x^2+3x+1-x^3+3x^2-3x+1-6(x^2+2x+1)
=6x^2+2-6x^2-12x-6
=-12x-4
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\(\left(x+3\right)\left(x^2-3x+9\right)-\left(x^3+54\right)\)
\(=x^3+3^3-x^3-54\)
\(=27-54\)
\(=-27\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(x+1\right)^2-\left(x-1\right)^2-3\left(x+1\right)\left(x-1\right)\)
\(=\left(x+1+x-1\right)\left(x+1-x+1\right)-3\left(x^2-1\right)\)
\(=2x.2-3x^2+1\)
\(=4x-3x^2+1\)
![](https://rs.olm.vn/images/avt/0.png?1311)
( x - 3 ) ( x2 + 3x + 9 ) - x ( x2 - 2 ) - 2 ( x - 1 )
= x3 - 27 - x3 + 2x - 2x + 2
= - 25
=x2-9-(x+6)2+12
=(x-x-6)(x+x+6)+3
=-12x-36+3
=-3(4x+11)