Final Answer
$x^2-3x-4$
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Step-by-step Solution
Problem to solve:
$\left(x+1\right)\left(x-4\right)$
Specify the solving method
1
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 ($L\times L$)
$\begin{matrix}(F\times F)\:=\:(x)(x)\\(O\times O)\:=\:(x)(-4)\\(I\times I)\:=\:(1)(x)\\(L\times L)\:=\:(1)(-4)\end{matrix}$
2
Then, combine the four terms in a sum
$(F\times F) + (O\times O) + (I\times I) + (L\times L)$
3
Substitute the values of the products
$x\cdot x-4x+1x+1\cdot -4$
4
Multiply $1$ times $-4$
$x\cdot x-4x+1x-4$
5
Any expression multiplied by $1$ is equal to itself
$x\cdot x-4x+x-4$
6
Combining like terms $-4x$ and $x$
$x\cdot x-3x-4$
7
When multiplying two powers that have the same base ($x$), you can add the exponents
$x^2-3x-4$
Final Answer
$x^2-3x-4$