 # Factor the polynomial. 81r^{2}-16t^{2}. John Stewart 2021-12-18 Answered
Factor the polynomial. $81{r}^{2}-16{t}^{2}$.
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Step 1
we have to factor the given polynomial.
$81{r}^{2}-16{t}^{2}$.
Step 2
$81{r}^{2}-16{t}^{2}$.
${\left(9r\right)}^{2}-{\left(4t\right)}^{2}$ now we will use the identity $\left({a}^{2}-{b}^{2}\right)=\left(a-b\right)\left(a+b\right)$
(9r+4t)(9r-4t)
therefore
$81{r}^{2}-16{t}^{2}=\left(9r+4t\right)\left(9r-4t\right)$

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Given,
$81{r}^{2}-16{t}^{2}$
On simplification, we get

$81{r}^{2}-16{t}^{2}=9\ast 9\ast r\ast r-4\ast 4\ast t\ast t$
$={9}^{2}\cdot {r}^{2}-{4}^{2}\cdot {t}^{2}$
$={\left(9r\right)}^{2}-{\left(4t\right)}^{2}$

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