Câu 107:
a: \(A=27+\left(x-3\right)\left(x^2+3x+9\right)\)
\(=27+x^3-3^3\)
\(=x^3\)
Thay x=-3 vào A, ta được:
\(A=\left(-3\right)^3=-27\)
b: \(B=\left(3x+1\right)\left(9x^2-3x+1\right)-\left(1-3x\right)\left(1+3x+9x^2\right)\)
\(=\left(3x\right)^3+1^3-\left(1^3-27x^3\right)\)
\(=27x^3+1-1+27x^3=54x^3\)
Khi x=10 thì \(B=54\cdot10^3=54\cdot1000=54000\)
c: ĐKXĐ: x<>1
\(C=\dfrac{x^3-1}{x^2-2x+1}\)
\(=\dfrac{\left(x-1\right)\left(x^2+x+1\right)}{\left(x-1\right)^2}\)
\(=\dfrac{x^2+x+1}{x-1}\)
Khi x=-1 thì \(C=\dfrac{\left(-1\right)^2+\left(-1\right)+1}{-1-1}=\dfrac{1}{-2}=-\dfrac{1}{2}\)
d: \(D=\dfrac{x^3+8}{x^2-2x+4}\)
\(=\dfrac{\left(x+2\right)\left(x^2-2x+4\right)}{x^2-2x+4}\)
\(=x+2\)
Khi x=-2 thì D=-2+2=0
Câu 105:
a: \(\left(x+3\right)\left(x^2-3x+9\right)-x^3\)
\(=x^3+3^3-x^3\)
=3^3
=27
b: \(\left(2+x\right)\left(4-2x+x^2\right)+x^3\)
\(=2^3+x^3+x^3\)
\(=8+2x^3\)
c: \(\left(3x-y\right)\left(9x^2+3xy+y^2\right)+y^3\)
\(=\left(3x\right)^3-y^3+y^3\)
\(=27y^3\)
d: \(\left(x-2y\right)\cdot\left(x^2+2xy+4y^2\right)+8y^3\)
\(=x^3-\left(2y\right)^3+8y^3\)
\(=x^3-8y^3+8y^3=x^3\)
