a: \(A=\left(x+3y\right)\left(x^2-3xy+9y^2\right)\)
\(=x^3+\left(3y\right)^3=x^3+27y^3\)
Khi x=y=1/2 thì \(A=\left(\frac12\right)^3+27\cdot\left(\frac12\right)^3=\frac18+\frac{27}{8}=\frac{28}{8}=\frac72\)
b: \(B=\left(25x^2+10xy+4y^2\right)\left(5x-2y\right)\)
\(=\left(5x-2y\right)\left\lbrack\left(5x\right)^2+5x\cdot2y+\left(2y\right)^2\right\rbrack\)
\(=\left(5x\right)^3-\left(2y\right)^3=125x^3-8y^3\)
Khi x=1/5; y=1/2 thì \(B=125\cdot\left(\frac15\right)^3-8\cdot\left(\frac12\right)^3=\frac{125}{125}-\frac88=1-1=0\)
c: \(x=1297\)
=>x-1=1296; x+1=1298
\(C=1296x-1298x^2+x^3\)
\(=x^3-x^2\left(x+1\right)+x\left(x-1\right)\)
\(=x^3-x^2-x^2+x^2-x=-x\)
=-1297
d: \(D=2x^4-61x^3-95x^2-31x+64\)
\(=2x^4-64x^3+3x^3-96x^2+x^2-32x+x-32+96\)
=(x-32)\(\left(2x^3+3x^2+x+1\right)\) +96
=96
