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

1 Answer
May 29, 2018

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

Explanation:

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