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\(a,\left(x+1\right)\left(x^2-x+1\right)-\left(x-1\right)\left(x^2+x+1\right)\) \(=x^3+1-x^3+1=2\)
\(b,x\left(x-4\right)\left(x+4\right)-\left(x^2+1\right)\left(x^2-1\right)\)
\(=x\left(x^2-16\right)-\left(x^4-1\right)=x^3-16x-x^4+1\) \(c,\left(x-3\right)\left(x+3\right)-\left(x+1\right)^2\)
\(=x^2-9-x^2-2x-1=-2x-10\)
\(d,\left(4x-3\right)\left(4x+3\right)-16x^2\)
\(=16x^2-9-16x^2=-9\)
\(e,\left(x+4\right)\left(x^2-4x+16\right)-x^3=x^3+64-x^3=64\)
Tìm GTNN của biểu thức :
\(x^2+2x+4\)
Đặt A = \(x^2+2x+4\)
\(\Leftrightarrow A=\left(x^2+2.x.1+1\right)+3\)
\(\Leftrightarrow A=\left(x+1\right)^2+3\)
Ta luôn có : \(\left(x+1\right)^2\ge0\forall x\)
Suy ra : \(\left(x+1\right)^2+3\ge3\forall x\)
Hay A\(\ge3\) với mọi x
Dấu "=" xảy ra khi \(x+1=0\Rightarrow x=-1\)
Nên : \(A_{min}=3khix=-1\)
a) \(4x^4+4x^3-x^2-x=4x^3\left(x+1\right)-x\left(x+1\right)\)
\(=\left(4x^3-x\right)\left(x+1\right)=x\left(4x^2-1\right)\left(x+1\right)\)
\(=x\left\{\left(2x\right)^2-1\right\}\left(x+1\right)=x\left(2x-1\right)\left(2x+1\right) \left(x+1\right)\)
c) \(x^4-4x^3+8x^2-16x+16=x^4+8x^2+16-\left(4x^3+16x\right)\)
\(=\left(x^2+4\right)^2-4x\left(x^2+4\right)=\left(x^2-4x+4\right)\left(x^2+4\right)=\left(x-2\right)^2\left(x^2+4\right)\)
b) \(x^6-x^4-9x^3+9x^2=x^4\left(x^2-1\right)-\left(9x^3-9x^2\right)\)
\(=x^4\left(x-1\right)\left(x+1\right)-9x^2\left(x-1\right)\)
\(=\left(x^5+x^4-9x^2\right)\left(x-1\right)=\left(x-1\right)x^2\left(x^3+x^2-9\right)\)
Bài 1 :
a, \(\left(x+3\right)^2+\left(x-3\right)^2+2\left(x^2-9\right)\)
\(=x^2+6x+9+x^2-6x+9+2x^2-18\)
\(=4x^2\)
b, \(\left(4x-1\right)^3-\left(4x-3\right)\left(16x^2+3\right)\)
\(=64x^3-32x^2+4x-16x^2+8x-1-64x^3-12x+48x^2+9=8\)
a) \(\left(x-3\right)\left(x+3\right)-\left(x+1\right)^2\) = \(x^2-9-\left(x^2+2x+1\right)\)
\(x^2-9-x^2-2x-1\) = \(-2x-10\)
b) \(\left(4x-3\right)\left(4x+3\right)-16x^2\) = \(16x^2-9-16x^2=-9\)
c) \(\left(x+4\right)\left(x^2-4x+16\right)-x^3\) = \(x^3-4x^2+16x+4x^2-16x+64-x^3\)
= \(64\)
\(a,\left(x-3\right)\left(x+3\right)-\left(x+1\right)^2=x^2-9-x^2-2x-1=-10-2x\) \(b,\left(4x-3\right)\left(4x+3\right)-16x^2=16x^2-9-16x^2=-9\)\(c,\left(x+4\right)\left(x^2-4x+16\right)-x^3=x^3+64-x^3=64\)