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Solve the product $\left(x+1\right)\left(x-4\right)$

Step-by-step Solution

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Final Answer

$x^2-3x-4$
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Step-by-step Solution

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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

$x^2-3x-4$

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1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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Main Topic: Integral Calculus

Integration assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

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