# Find the binomial that completes the factorization. 5s^4+5000st^3= 5s(s^3+1000t^3)

Find the binomial that completes the factorization.
$5{s}^{4}+5000s{t}^{3}=5s\left({s}^{3}+1000{t}^{3}\right)$
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Step 1
Given:
$5{s}^{4}+5000s{t}^{3}=5s\left({s}^{3}+1000{t}^{3}\right)$
We know that
${a}^{3}+{b}^{3}=\left(a+b\right)\left({a}^{2}+ab+{b}^{2}\right)$
So,
$\left({s}^{3}+1000{t}^{3}\right)=\left({s}^{3}+{\left(10t\right)}^{3}\right)$
Step 2
$\left({s}^{3}+{\left(10t\right)}^{3}\right)=\left(s+10t\right)\left({s}^{2}-\left(s\right)\left(10t\right)+{\left(10t\right)}^{2}\right)$
$=\left(s+10t\right)\left({s}^{2}-10st+{10}^{2}{t}^{2}\right)$
Hence
$5{s}^{4}+5000s{t}^{3}=\left(s=10t\right)\left({s}^{2}-10st+{10}^{2}{t}^{2}\right)$