We can multiply the polynomials $\left(x+1\right)\left(x-4\right)$ by using the FOIL method. The acronym F O I L stands for multiplying the terms in each bracket in the following order: First by First ($F\times F$), Outer by Outer ($O\times O$), Inner by Inner ($I\times I$), Last by Last ($L\times L$)

Then, combine the four terms in a sum

Substitute the values of the products

Multiply $1$ times $-4$

Any expression multiplied by $1$ is equal to itself

Combining like terms $-4x$ and $x$

When multiplying two powers that have the same base ($x$), you can add the exponents