Worth 20 points and ! some steps to rewrite the expression x3 − 9x + x2 − 9 as a product of three factors are shown below: step 1: x3 − 9x + x2 − 9 step 2: x3 + x2 − 9x − 9 step 3: x2(x + 1) − 9(x + 1) which of the following best shows the next two steps to rewrite the expression? step 4: (x2 + 9)(x + 1); step 5: (x + 3)(x + 3)(x + 1) step 4: (x2 − 9)(x + 1); step 5: (x + 3)(x + 3)(x + 1) step 4: (x2 + 9)(x + 1); step 5: (x − 3)(x + 3)(x + 1) step 4: (x2 − 9)(x + 1); step 5: (x − 3)(x + 3)(x + 1)

The correct option is D) Step 4:; Step 5: (x − 3)(x + 3)(x + 1).

Step-by-step explanation:

Consider the provided expression.

Step 1: The provided expression is:

Step 2:

Step 3:

Step 4:

This can be written s:

Step 5: Use the formula,

Hence, the correct option is D) Step 4: ; Step 5: (x − 3)(x + 3)(x + 1).

2x • (x^3y^3 + 2)

Step-by-step explanation:

4x +  (2x3y • y) • x) • y)

Pulling out like terms :

3.1     Pull out like factors :

  2x4y3 + 4x  =   2x • (x3y3 + 2)

Trying to factor as a Sum of Cubes :

3.2      Factoring:  x3y3 + 2

Theory : A sum 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 :  2  is not a cube !!

Ruling : Binomial can not be factored as the difference of two perfect cube

Final result :

 2x • (x^3y^3 + 2)

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