a) Ta có: \(A=x^2+2xy+y^2-2x-2y+15\)
\(=\left(x+y\right)^2-2\left(x+y\right)+15\)
\(=\left(x+y\right)\left(x+y-2\right)+15\)
\(=5\cdot\left(5-2\right)+15\)
=30
c) Ta có: x=79
nên x+1=80
Ta có: \(P\left(x\right)=x^7-80x^6+80x^5-80x^4+...+80x+15\)
\(=x^7-x^6\left(x+1\right)+x^5\left(x+1\right)-x^4\left(x+1\right)+...+x\left(x+1\right)+15\)
\(=x^7-x^7-x^6+x^6+x^5-x^5-x^4+...+x^2+x+15\)
=x+15
=79+15
=94
d) Ta có: x=11
nên x-1=10
Ta có: \(Q\left(x\right)=x^{14}-10x^{13}-10x^{12}-10x^{11}-...-10x^2-10x+10\)
\(=x^{14}-x^{13}\left(x-1\right)-x^{12}\left(x-1\right)-x^{11}\left(x-1\right)-...-x^2\left(x-1\right)-x\left(x-1\right)+x-1\)
\(=x^{14}-x^{14}+x^{13}-x^{13}+x^{12}-x^{12}+x^{11}-...-x^3+x^2-x^2+x+x-1\)
=2x-1
=21
