# Express as a polynomial. (r2+8r−2)(r2+3r−1)

Kathy Williams

## Answered question

2021-12-11

Express as a polynomial. $({r}^{2}+8r-2)({r}^{2}+3r-1)$

### Answer & Explanation

Step 1

Given expression:

$({r}^{2}+8r-2)({r}^{2}+3r-1)$

Step 2

Consider,

$({r}^{2}+8r-2)({r}^{2}+3r-1)={r}^{2}({r}^{2}+3r-1)+8r({r}^{2}+3r-1)-2({r}^{2}+3r-1)$...Use the distributive property.

$=[{r}^{2}\left({r}^{2}\right)+{r}^{2}\left(3r\right)+{r}^{2}(-2)]+[\left(8r\right)\left({r}^{2}\right)+\left(28r\right)\left(3r\right)+\left(8r\right)(-2)]-[2{r}^{2}+\left(2\right)\left(3r\right)-\left(2\right)\left(1\right)]$

$={r}^{4}+3{r}^{3}-2{r}^{2}+8{r}^{3}+24{r}^{2}-16r-2{r}^{2}-6r+2$

$={r}^{4}+(3{r}^{3}+8{r}^{3})+(-2{r}^{2}+24{r}^{2}-2{r}^{2})+(-16r-6r)+2$...Collect like terms together.

$={r}^{4}+11{r}^{3}+20{r}^{2}-22r+2$

Thus,

$({r}^{2}+8r-2)({r}^{2}+3r-1)={r}^{4}+11{r}^{3}+20{r}^{2}-22r+2$

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