Use polynomial identities to factor 64 + 27a^3

Rewrite

27

a

3

as

(

3

a

)

3

.

(

3

a

)

3

−

64

Rewrite

64

as

4

3

.

(

3

a

)

3

−

4

3

Since both terms are perfect cubes, factor using the difference of cubes formula,

a

3

−

b

3

=

(

a

−

b

)

(

a

2

+

a

b

+

b

2

)

where

a

=

3

a

and

b

=

4

.

(

3

a

−

4

)

(

(

3

a

)

2

+

3

a

⋅

4

+

4

2

)

Step-by-step explanation:

(3a+4)(9a^2-12a+16)

Step-by-step explanation:

It's a perfect square :)

arrange the equations with like terms in columns.

analyze the coefficients of x or y.

add the equations and solve for the remaining variable.

substitute the value into either equation and solve.

check the solution.

step-by-step explanation: