Math, asked by rathakishoresoren957, 10 months ago

54x
 {54x}^{3}   +  {128y}^{3}
(a
{x}^{3}  +  {y}^{3}

Answers

Answered by abhishekmishra737007
0

Answer:

Explanation:

When factoring,

Step 1: Always factor out a GCF first, if possible.

In this particular problem, we can factor out 2:

54

x

3

2

y

3

=

2

(

27

x

3

y

3

)

Step 2: Count the number of terms:

—if 2 terms, check if problem is:

difference of squares

(

a

2

b

2

)

, which factors into

(

a

b

)

(

a

+

b

)

difference of cubes

(

a

3

b

3

)

, which factors into

(

a

b

)

(

a

2

+

a

b

+

b

2

)

sum of cubes

(

a

3

+

b

3

)

, which factors into

(

a

+

b

)

(

a

2

a

b

+

b

2

)

(

27

x

3

y

3

)

is a difference of cubes:

27

x

3

=

(

3

x

)

3

y

3

=

(

y

)

3

Plugging these values into the difference of cubes formula:

(

a

3

b

3

)

=

(

a

b

)

(

a

2

+

a

b

+

b

2

)

(

(

3

x

)

3

(

(

y

)

3

)

=

(

(

3

x

)

(

y

)

)

(

(

3

x

)

2

+

(

3

x

)

(

y

)

+

(

y

)

2

)

27

x

3

y

3

=

(

3

x

y

)

(

9

x

2

+

3

x

y

+

y

2

)

Putting it all together:

54

x

3

2

y

3

=

2

(

27

x

3

y

3

)

54

x

3

2

y

3

=

2

(

3

x

y

)

(

9

x

2

+

3

x

y

+

y

2

)

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