ðŸ‘‰ Try now NerdPal! Our new math app on iOS and Android

# Expand the expression $\left(a-4\right)^3$

## Step-by-step Solution

Go!
Math mode
Text mode
Go!
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

###  Videos

$a^3-12a^2+48a-64$
Got another answer? Verify it here!

##  Step-by-step Solution 

Specify the solving method

1

The cube of a binomial (difference) is equal to the cube of the first term, minus three times the square of the first by the second, plus three times the first by the square of the second, minus the cube of the second term. In other words: $(a-b)^3=a^3-3a^2b+3ab^2-b^3 = (a)^3+3(a)^2(-4)+3(a)(-4)^2+(-4)^3 =$

$a^3+3\cdot -4a^2+3\cdot {\left(-4\right)}^2a+{\left(-4\right)}^3$

Learn how to solve special products problems step by step online.

$a^3+3\cdot -4a^2+3\cdot {\left(-4\right)}^2a+{\left(-4\right)}^3$

Learn how to solve special products problems step by step online. Expand the expression (a-4)^3. The cube of a binomial (difference) is equal to the cube of the first term, minus three times the square of the first by the second, plus three times the first by the square of the second, minus the cube of the second term. In other words: (a-b)^3=a^3-3a^2b+3ab^2-b^3 = (a)^3+3(a)^2(-4)+3(a)(-4)^2+(-4)^3 =. Multiply 3 times -4. Calculate the power {\left(-4\right)}^2. Multiply 3 times 16.

$a^3-12a^2+48a-64$

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Product of Binomials with Common TermFOIL MethodFactorFind the derivativeFind the integral

SnapXam A2

Go!
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

### Main Topic: Special Products

Special products is the multiplication of algebraic expressions that follow certain rules and patterns, so you can predict the result without necessarily doing the multiplication.