Simplify:
4km^2(8km^2 + 2k^2m + 5k)4km2(8km2+2k2m+5k)
Distribute 4km^24km2 by multiplying by each of the terms in parentheses.
(4km^2*8km^2) + (4km^2*2k^2m) + (4km^2*5k)(4km2⋅8km2)+(4km2⋅2k2m)+(4km2⋅5k)
Recombine the constants and variables.
(4*8*k*k*m^2*m^2) + (4*2*k*k^2*m^2*m) + (4*5*k*k*m^2)(4⋅8⋅k⋅k⋅m2⋅m2)+(4⋅2⋅k⋅k2⋅m2⋅m)+(4⋅5⋅k⋅k⋅m2)
Multiply the constants.
(32*k*k*m^2*m^2) + (8*k*k^2*m^2*m) + (20*k*k*m^2)(32⋅k⋅k⋅m2⋅m2)+(8⋅k⋅k2⋅m2⋅m)+(20⋅k⋅k⋅m2)
Apply product rule: a^ma^n=a^(m+n)aman=am+n
Recall that no exponent is understood to be 11.
(32*k^(1+1)m^(2+2)) + (8*k^(1+2)*m^(2+1)) + (20*k^(1+1)*m^2)(32⋅k1+1m2+2)+(8⋅k1+2⋅m2+1)+(20⋅k1+1⋅m2)
Simplify.
32k^2m^4 + 8k^3m^3 + 20k^2m^232k2m4+8k3m3+20k2m2
