\(x\left(1+5x\right)\)

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

\(\left(x^2+1\right)\left(2x+1\right)\)

 a x + 5x^2

=x(1+ 5x)

b x^2 – 9

=x^2 – 3^2

=(x-3)(x+3)

c 2x^3 + x^2 + 2x + 1

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

=x^2(2x + 1)+(2x + 1)

=(2x + 1)(x^2+1)

\(a,=4x\left(x+2\right)\\ b,=\left(x-3\right)\left(x+3\right)\\ c,=x^2\left(2x-3\right)+\left(2x-3\right)=\left(2x-3\right)\left(x^2+1\right)\)

a)4x²+8x                     b)x²-9

=4x(x+2)                      =x²-3²

                                     =(x-3)(x+3)

c)2x³-3x²+2x-3

=2x³+2x-(3x²+3)

=2x(x²+1)-3(x²+1)

=(2x-3)(x²+1)

\(a,\left(x-2\right)^2=x^2-2.x.2+2^2=x^2-4x+4\\ b,\left(x+1\right)^3=x^3+3.x^2.1+3.x.1^2+1^3=x^3+3x^2+3x+1\\ c,x^2-5x^2=-4x^2\)

\(a,=12-3x+4x-x^2+x^2-2x=12-x\\ b,=x^2-2x+1-x^2+4=-2x+5\)

\(a,=x^2-3x-10-x^2+3x=-10\\ b,=\left(x+1\right)\left(x+1-x+1\right)=2\left(x+1\right)=2x+2\)

a, Với x khác 1 

\(A=\dfrac{x^2+x+1-3x^2+2x\left(x-1\right)}{\left(x-1\right)\left(x^2+x+1\right)}=\dfrac{1-x}{\left(x-1\right)\left(x^2+x+1\right)}=-\dfrac{1}{x^2+x+1}\)

b, Ta có \(x^2+x+1=\left(x+\dfrac{1}{2}\right)^2+\dfrac{3}{4}>0\Rightarrow\dfrac{-1}{\left(x+\dfrac{1}{2}\right)^2+\dfrac{3}{4}}< 0\)

Vậy với x khác 1 thì bth A luôn nhận gtri âm 

a) \(A=\left(x-1\right).\left(x+1\right)+\left(x+2\right).\left(x^2+2x+4\right)-x.\left(x^2+x+2\right)\)

\(=x^2-1+x^3+2x^2+4x+2x^2+4x+8-x^3-x^2-2x\)

\(=\left(x^3-x^3\right)+\left(x^2+2x^2+2x^2-x^2\right)+\left(4x+4x-2x\right)+\left(-1+8\right)\)

\(=4x^2+6x+7\)

b) Thay vào ta được

\(A=4.\left(\frac{1}{2}\right)^2+6.\frac{1}{2}+7=1+3+7=11\)