Question

Factories the following 8x +64y
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Answer 1

Answer:

Step by Step Solution

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STEP

1

:

Equation at the end of step 1

(8 • (x3)) - 26y3

STEP

2

:

Equation at the end of step

2

:

23x3 - 26y3

STEP

3

:

STEP

4

:

Pulling out like terms

4.1 Pull out like factors :

8x3 - 64y3 = 8 • (x3 - 8y3)

Trying to factor as a Difference of Cubes:

4.2 Factoring: x3 - 8y3

Theory : A difference of two perfect cubes, a3 - b3 can be factored into

(a-b) • (a2 +ab +b2)

Proof : (a-b)•(a2+ab+b2) =

a3+a2b+ab2-ba2-b2a-b3 =

a3+(a2b-ba2)+(ab2-b2a)-b3 =

a3+0+0+b3 =

a3+b3

Check : 8 is the cube of 2

Check : x3 is the cube of x1

Check : y3 is the cube of y1

Factorization is :

(x - 2y) • (x2 + 2xy + 4y2)

Trying to factor a multi variable polynomial :

4.3 Factoring x2 + 2xy + 4y2

Try to factor this multi-variable trinomial using trial and error

Factorization fails

Final result :

8 • (x - 2y) • (x2 + 2xy + 4y2

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