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.

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

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