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{\displaystyle =(x^{7}-x)+(x^{5}-x^{2})+x^{2}+x+1}
{\displaystyle =x(x^{6}-1)+x^{2}(x^{3}-1)+(x^{2}+x+1)}
{\displaystyle =x(x^{3}+1)(x^{3}-1)+x^{2}(x^{3}-1)+(x^{2}+x+1)}
{\displaystyle =(x^{4}+x^{2}+x)(x-1)(x^{2}+x+1)+(x^{2}+x+1)}
{\displaystyle =(x^{2}+x+1)(x^{5}-x^{4}+x^{3}-x+1)}
b)x3-2x2-4xy2+x
=x(x2-2x-4y2+1)
=x[(x2-2x+1)-4y2]
=x[(x-1)2-4y2]
=x(x-1-2y)(x-1+2y)
c) (x+2)(x+3)(x+4)(x+5)-8
=[(x+2)(x+5)][(x+3)(x+4)]-8
=(x2+5x+2x+10)(x2+4x+3x+12)-8
=(x2+7x+10)(x2+7x+12)-8
đặt x2+7x+10 =a ta có
a(a+2)-8
=a2+2a-8
=a2+4a-2a-8
=(a2+4a)-(2a+8)
=a(a+4)-2(a+4)
=(a+4)(a-2)
thay a=x2+7x+10 ta đc
(x2+7x+10+4)(x2+7x+10-2)
=(x2+7x+14)(x2+7x+8)
bài 2 x3-x2y+3x-3y
=(x3-x2y)+(3x-3y)
=x2(x-y)+3(x-y)
=(x-y)(x2+3)
\(x^4+x^3+x^2-1\)
\(=x^3\left(x+1\right)+\left(x^2-1\right)\)
\(=x^3\left(x+1\right)+\left(x-1\right)\left(x+1\right)\)
\(=\left(x^3+x-1\right)\left(x+1\right)\)
\(a,\left|x+3,4\right|+\left|x+2,4\right|+\left|x+7,2\right|=4x\)
\(\left|x+3,4\right|\ge0;\left|x+2,4\right|\ge0;\left|x+7,2\right|\ge0\)
\(< =>\left|x+3,4\right|+\left|x+2,4\right|+\left|x+7,2\right|>0\)
\(< =>4x>0\)
\(x>0\)
\(\hept{\begin{cases}\left|x+3,4\right|=x+3,4\\\left|x+2,4\right|=x+2,4\\\left|x+7,2\right|=x+7,2\end{cases}}\)
\(x+3,4+x+2,4+x+7,2=4x\)
\(x=13\left(TM\right)\)
\(b,3^{n+3}+3^{n+1}+2^{n+3}+2^{n+2}\)
\(3^n.27+3^n.3+2^n.8+2^n.4\)
\(3^n.30+2^n.12\)
\(\hept{\begin{cases}3^n.30⋮6\\2^n.12⋮6\end{cases}}\)
\(< =>3^n.30+2^n.12⋮6< =>VP⋮6\)
Giải :
8ax - 4ay - 2x + y
= 2x( 4a - 1 ) - y( 4a - 1 )
= ( 2x - y )( 4a - 1 )
8ax - 4ay - 2x + y
= (8ax - 2x) - (4ay - y)
= 2x(4a - 1) - y(4a - 1)
= (2x - y)(4a - 1)