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

Tolnaio 2020-11-24 Answered
Find the binomial that completes the factorization.
5s4+5000st3=5s(s3+1000t3)
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Expert Answer

Sally Cresswell
Answered 2020-11-25 Author has 91 answers
Step 1
Given:
5s4+5000st3=5s(s3+1000t3)
We know that
a3+b3=(a+b)(a2+ab+b2)
So,
(s3+1000t3)=(s3+(10t)3)
Step 2
(s3+(10t)3)=(s+10t)(s2(s)(10t)+(10t)2)
=(s+10t)(s210st+102t2)
Hence
5s4+5000st3=(s=10t)(s210st+102t2)
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