Find the binomial that completes the factorization.

$5{s}^{4}+5000s{t}^{3}=5s({s}^{3}+1000{t}^{3})$

Tolnaio
2020-11-24
Answered

Find the binomial that completes the factorization.

$5{s}^{4}+5000s{t}^{3}=5s({s}^{3}+1000{t}^{3})$

You can still ask an expert for help

Sally Cresswell

Answered 2020-11-25
Author has **91** answers

Step 1

Given:

$5{s}^{4}+5000s{t}^{3}=5s({s}^{3}+1000{t}^{3})$

We know that

${a}^{3}+{b}^{3}=(a+b)({a}^{2}+ab+{b}^{2})$

So,

$({s}^{3}+1000{t}^{3})=({s}^{3}+{\left(10t\right)}^{3})$

Step 2

$({s}^{3}+{\left(10t\right)}^{3})=(s+10t)({s}^{2}-\left(s\right)\left(10t\right)+{\left(10t\right)}^{2})$

$=(s+10t)({s}^{2}-10st+{10}^{2}{t}^{2})$

Hence

$5{s}^{4}+5000s{t}^{3}=(s=10t)({s}^{2}-10st+{10}^{2}{t}^{2})$

Given:

We know that

So,

Step 2

Hence

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