a)
\(A=\dfrac{35^3+13^3}{48}-35\cdot13\\ =\dfrac{\left(35+13\right)\left(35^2+35\cdot13+13^2\right)}{48}-35\cdot13\\ =\dfrac{48\cdot\left(35^2-35\cdot13+13^2\right)}{48}-35\cdot13\\ =35^2-35\cdot13+13^2-35\cdot13\\ =35^2-2\cdot35\cdot13+13^2\\ =\left(35-13\right)^2\\ =22^2=484\)
b)
\(B=\dfrac{68^3-52^3}{16}+68\cdot52\\ =\dfrac{\left(68-52\right)\left(68^2+68\cdot52+52^2\right)}{16}+68\cdot52\\ =\dfrac{16\cdot\left(68^2+68\cdot52+52^2\right)}{16}+68\cdot52\\ =68^2+68\cdot52+52^2+68\cdot52\\ =68^2+2\cdot68\cdot52+52^2\\ =\left(68+52\right)^2\\ =120^2=14400\)
c)
\(C=\dfrac{85^3-15^3}{70}-3\cdot85\cdot15\\ =\dfrac{\left(85-15\right)\cdot\left(85^2+85\cdot15+15^2\right)}{70}-3\cdot85\cdot15\\ =\dfrac{70\cdot\left(85^2+85\cdot15+15^2\right)}{70}-3\cdot85\cdot15\\ =85^2+85\cdot15+15^2-3\cdot85\cdot15\\ =85^2-2\cdot85\cdot15+15^2\\ =\left(85-15\right)^2\\ =70^2=4900\)
a: \(A=\dfrac{35^3+13^3}{48}-35\cdot13\)
\(=\dfrac{\left(35+13\right)\left(35^2-35\cdot13+13^2\right)}{48}-35\cdot13\)
\(=35^2-35\cdot13+13^2-35\cdot13\)
\(=35^2-2\cdot35\cdot13+13^2=\left(35-13\right)^2=22^2=484\)
b: \(B=\dfrac{68^3-52^3}{16}+68\cdot52\)
\(=\dfrac{\left(68-52\right)\left(68^2+68\cdot52+52^2\right)}{16}+68\cdot52\)
\(=68^2+68\cdot52+52^2+68\cdot52\)
\(=68^2+2\cdot68\cdot52+52^2\)
\(=\left(68+52\right)^2=120^2=14400\)
c: \(C=\dfrac{85^3-15^3}{70}-3\cdot85\cdot15\)
\(=\dfrac{\left(85-15\right)\left(85^2+85\cdot15+15^2\right)}{70}-3\cdot85\cdot15\)
\(=85^2+85\cdot15+15^2-3\cdot85\cdot15\)
\(=85^2-2\cdot85\cdot15+15^2=\left(85-15\right)^2=70^2=4900\)
