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![](https://rs.olm.vn/images/avt/0.png?1311)
a) Kết quả N = (x + 1)(x + 2);
b) Kết quả N = 2(x + 3)(x - 3).
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\Leftrightarrow\dfrac{x+1}{\left(x-3\right)\left(x+2\right)\cdot B}=\dfrac{\left(x-1\right)\left(x+1\right)}{\left(x-1\right)^2}\)
\(\Leftrightarrow B=\dfrac{x-1}{\left(x-3\right)\left(x+2\right)}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Lời giải:
1.
$M=(x^2+6x+9)+(x^2-9)-2(x^2-2x-8)$
$=x^2+6x+9+x^2-9-2x^2+4x+16=(x^2+x^2-2x^2)+(6x+4x)+(9-9+16)$
$=10x+16=5(2x+1)+11=5.0+11=11$
2.
$V=(9x^2+24x+16)-(x^2-16)-10x=9x^2+24x+16-x^2+16-10x$
$=(9x^2-x^2)+(24x-10x)+(16+16)=8x^2+14x+32$
$=8(\frac{-1}{10})^2+14.\frac{-1}{10}+32=\frac{767}{25}$
3.
$P=(x^2+2x+1)-(4x^2-4x+1)+3(x^2-4)$
$=x^2+2x+1-4x^2+4x-1+3x^2-12$
$=(x^2-4x^2+3x^2)+(2x+4x)+(1-1-12)$
$=6x-12=6.1-12=-6$
4.
$Q=(x^2-9)+(x^2-4x+4)-2x^2+8x$
$=x^2-9+x^2-4x+4-2x^2+8x$
$=(x^2+x^2-2x^2)+(-4x+8x)-9+4$
$=4x-5=4(-1)-5=-9$
![](https://rs.olm.vn/images/avt/0.png?1311)
\(2005^3-1=\left(2005-1\right)\left(2005^2+2005+1\right)=2004\times\left(2005^2+2005+1\right)⋮2004\left(\text{đ}pcm\right)\)
\(2005^3+125=\left(2005+5\right)\left(2005^2-2005\times5+5^2\right)=2010\times\left(2005^2-2005\times5+5^2\right)⋮2010\)
\(x^6+1=\left(x^2+1\right)\left(x^4-x^2+1\right)⋮x^2+1\left(\text{đ}pcm\right)\)
\(x^6-y^6=\left(x^2-y^2\right)\left(x^4+x^2y^2+y^2\right)=\left(x-y\right)\left(x+y\right)\left(x^4+x^2y^2+y^4\right)⋮x-y;x+y\left(\text{đ}pcm\right)\)
Tìm được A = 10 ( x 2 + 1 ) ( x 2 − 1 ) 2