How do you find the product #4km^2(8km^2+2k^2m+5k)#?

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Answer 1 · 2018-05-29T23:36:04

#4km^2(8km^2 + 2k^2m + 5k)=color(blue)(32k^2m^4 + 8k^3m^3 + 20k^2m^2#

Simplify:

#4km^2(8km^2 + 2k^2m + 5k)#

Distribute #4km^2# by multiplying by each of the terms in parentheses.

#(4km^2*8km^2) + (4km^2*2k^2m) + (4km^2*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)#

Multiply the constants.

#(32*k*k*m^2*m^2) + (8*k*k^2*m^2*m) + (20*k*k*m^2)#

Apply product rule: #a^ma^n=a^(m+n)#

Recall that no exponent is understood to be #1#.

#(32*k^(1+1)m^(2+2)) + (8*k^(1+2)*m^(2+1)) + (20*k^(1+1)*m^2)#

Simplify.

#32k^2m^4 + 8k^3m^3 + 20k^2m^2#