a) ta có : \(M=\left(a+b\right)^3+2a^2+4ab+2b^2\)
\(M=\left(a+b\right)^3+2\left(a^2+2ab+b^2\right)=\left(a+b\right)^3+2\left(a+b\right)^2\)
\(M=\left(7\right)^3+2.\left(7\right)^2=343+98=441\) vậy \(M=441\) khi \(a+b=7\)
b) ta có : \(N=\left(a-b\right)^3-a^2+2ab-b^2\)
\(N=\left(a-b\right)^3-\left(a^2-2ab+b^2\right)=\left(a-b\right)^3-\left(a-b\right)^2\)
\(N=\left(5\right)^3-\left(5\right)^2=125-25=100\) vậy \(N=100\) khi \(a-b=5\)
c) ta có : \(\left(a-b\right)^2=a^2-2ab+b^2=a^2+2ab+b^2-4ab\)
\(=\left(a+b\right)^2-4ab=\left(5\right)^2-4.2=25-8=17\)
vậy \(\left(a-b\right)^2=17\) khi \(a+b=5\) và \(ab=2\)
