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

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

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Answer 1 · 2018-05-29T23:36:04

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

Explanation:

Simplify:

$4 k m^{2} (8 k m^{2} + 2 k^{2} m + 5 k)$ $4km^2(8km^2 + 2k^2m + 5k)$

Distribute $4 k m^{2}$ $4km^2$ by multiplying by each of the terms in parentheses.

$(4 k m^{2} \cdot 8 k m^{2}) + (4 k m^{2} \cdot 2 k^{2} m) + (4 k m^{2} \cdot 5 k)$ $(4km^2*8km^2) + (4km^2*2k^2m) + (4km^2*5k)$

Recombine the constants and variables.

$(4 \cdot 8 \cdot k \cdot k \cdot m^{2} \cdot m^{2}) + (4 \cdot 2 \cdot k \cdot k^{2} \cdot m^{2} \cdot m) + (4 \cdot 5 \cdot k \cdot k \cdot m^{2})$ $(4*8*k*k*m^2*m^2) + (4*2*k*k^2*m^2*m) + (4*5*k*k*m^2)$

Multiply the constants.

$(32 \cdot k \cdot k \cdot m^{2} \cdot m^{2}) + (8 \cdot k \cdot k^{2} \cdot m^{2} \cdot m) + (20 \cdot k \cdot k \cdot m^{2})$ $(32*k*k*m^2*m^2) + (8*k*k^2*m^2*m) + (20*k*k*m^2)$

Apply product rule: $a^{m} a^{n} = a^{m + n}$ $a^ma^n=a^(m+n)$

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

$(32 \cdot k^{1 + 1} m^{2 + 2}) + (8 \cdot k^{1 + 2} \cdot m^{2 + 1}) + (20 \cdot k^{1 + 1} \cdot m^{2})$ $(32*k^(1+1)m^(2+2)) + (8*k^(1+2)*m^(2+1)) + (20*k^(1+1)*m^2)$

Simplify.

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

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

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