(m+4)^2 - (m-3)(m+3)=m^2+8m+16-(m^2 -9)=m^2 +8m+16-m^2+9=8m+25
(n+5)^2 - n(n-7)=n^2+10n+25-n^2 +7n=17n+25
(6-n)(n+6)+(n-4)^2=6n+36-n^2 -6n+n^2 -8n+16=52-8n
(m+n)(m-n)(m^2-n^2)+2m^2 n^2=(m^2 -n^2)*(m^2-n^2)+2m^2 n^2=(m^2 - n^2)^2 +2m^2 n^2=m^4 -2m^2 n^2 +n^4 +2m^2 n^2=m^4 +n^4
(a+3)(a-3)(a-3)(a+3)+18a^2=(a+3)^2 * (a-3)^2 +18a^2= ((a+3)*(a*3))^2 +18a^2=(a^2 -9)^2 +18a^2=a^4 -18a^2 +81+18a^2=a^4 +81