Question

Multiply. Write the result in standard form.(2 + 1)(3^4 + 7 + 2)

Answer 1

To multiply polynomials, we use the distributive law

`\begin{gathered} (2x+1)(3x^4+7x+2)=(2x+1)(3x^4)+(2x+1)(7x)+(2x+1)(2) \\ =2x(3x^4)+1(3x^4)+2x(7x)+1(7x)+2x(2)+1(2)_{} \\ =6x^5+3x^4+14x^2+7x+4x+2 \end{gathered}`

The last part follows by the laws of exponentials, finally we combine like terms

`\begin{gathered} 6x^5+3x^4+14x^2+7x+4x+2=6x^5+3x^4+14x^2+(7+4)x+2 \\ =6x^5+3x^4+14x^2+11x+2 \end{gathered}`