How do you multiply polynomials (x^2 + 2x - 1)(x^2 + 2x + 5)?

Mar 31, 2018

${x}^{4} + 4 {x}^{3} + 6 {x}^{2} + 8 x - 5$

Explanation:

Just use a modified version of foil or a table

${x}^{2} \left({x}^{2} + 2 x + 5\right) = {x}^{4} + 2 {x}^{3} + 5 {x}^{2}$

$2 x \left({x}^{2} + 2 x + 5\right) = 2 {x}^{3} + 2 {x}^{2} + 10 x$

$- 1 \left({x}^{2} + 2 x + 5\right) = - {x}^{2} - 2 x - 5$

${x}^{4} + 2 {x}^{3} + 5 {x}^{2} + 2 {x}^{3} + 2 {x}^{2} + 10 x - {x}^{2} - 2 x - 5$

${x}^{4} + \textcolor{red}{2 {x}^{3} + 2 {x}^{3}} + \textcolor{b l u e}{5 {x}^{2} + 2 {x}^{2} - {x}^{2}} + \textcolor{\pi n k}{10 x - 2 x} - 5$

${x}^{4} + \textcolor{red}{4 {x}^{3}} + \textcolor{b l u e}{6 {x}^{2}} + \textcolor{\pi n k}{8 x} - 5$

Mar 31, 2018

${x}^{4} + 4 {x}^{3} + 8 {x}^{2} + 8 x - 5$

Explanation:

Given-

$\left({x}^{2} + 2 x - 1\right) \left({x}^{2} + 2 x + 5\right)$

$\left({x}^{2} \times {x}^{2}\right) + \left(2 x \times {x}^{2}\right) - \left(1 \times {x}^{2}\right) + \left({x}^{2} \times 2 x\right) + \left(2 x \times 2 x\right) - \left(1 \times 2 x\right) + \left({x}^{2} \times 5\right) + \left(2 x \times 5\right) - \left(1 \times 5\right)$

${x}^{4} + 2 {x}^{3} - {x}^{2} + 2 {x}^{3} + 4 {x}^{2} - 2 x + 5 {x}^{2} + 10 x - 5$

${x}^{4} + 2 {x}^{3} + 2 {x}^{3} - {x}^{2} + 4 {x}^{2} + 5 {x}^{2} - 2 x + 10 x - 5$

${x}^{4} + 4 {x}^{3} + 8 {x}^{2} + 8 x - 5$