Question

simplify (9 x2_16x - 4 )- 15x - 12 x2+5)​

Answer 1

Answer:

Equation at the end of step 1

 (((5 • (x3)) +  22x2) -  15x) -  12  

Equation at the end of step  2  

 ((5x3 +  22x2) -  15x) -  12

STEP  3 : Checking for a perfect cube

3.1    5x3+4x2-15x-12  is not a perfect cube

Trying to factor by pulling out :

3.2      Factoring:  5x3+4x2-15x-12  

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  -15x-12  

Group 2:  5x3+4x2  

Pull out from each group separately :

Group 1:   (5x+4) • (-3)

Group 2:   (5x+4) • (x2)

              -------------------

Add up the two groups :

              (5x+4)  •  (x2-3)  

Which is the desired factorization

Trying to factor as a Difference of Squares:

3.3      Factoring:  x2-3  

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 3 is not a square !!

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

Final result :

 (x2 - 3) • (5x + 4)

Step-by-step explanation:

i hope this helped