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Expand the expression $\left(6a-2b\right)^3$

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 Final answer to the problem

$216a^3-216a^2b+18a\left(-2b\right)^2+\left(-2b\right)^3$
Got another answer? Verify it here!

 Step-by-step Solution 

How should I solve this problem?

• Choose an option
• Product of Binomials with Common Term
• FOIL Method
• Find the integral
• Find the derivative
• Factor
• Integrate by partial fractions
• Integrate by substitution
• Integrate by parts
• Integrate using tabular integration
Can't find a method? Tell us so we can add it.
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: $(a-b)^3=a^3-3a^2b+3ab^2-b^3 = (6a)^3+3(6a)^2(-2b)+3(6a)(-2b)^2+(-2b)^3 =$

$\left(6a\right)^3+3\cdot -2\left(6a\right)^2b+3\cdot 6a\left(-2b\right)^2+\left(-2b\right)^3$

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

$\left(6a\right)^3+3\cdot -2\left(6a\right)^2b+3\cdot 6a\left(-2b\right)^2+\left(-2b\right)^3$

Learn how to solve special products problems step by step online. Expand the expression (6a-2b)^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 = (6a)^3+3(6a)^2(-2b)+3(6a)(-2b)^2+(-2b)^3 =. Multiply 3 times -2. Multiply 3 times 6. The power of a product is equal to the product of it's factors raised to the same power.

 Final answer to the problem

$216a^3-216a^2b+18a\left(-2b\right)^2+\left(-2b\right)^3$

 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

SnapXam A2

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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.