Question

tan²(3x³+3x²+x/2+15)
​

Answer 1

Answer:

tan²(3x³+3x²+x/2+15)=tan²(3x³+3x²+x/17)

Step-by-step explanation:

STEP

1

:

Equation at the end of step 1

 3x2 -  15

STEP

2

:

STEP

3

:

Pulling out like terms

3.1     Pull out like factors :

  3x2 - 15  =   3 • (x2 - 5)

Trying to factor as a Difference of Squares:

3.2      Factoring:  x2 - 5

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 : 5 is not a square !!

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

Final result :

 3 • (x2 - 5)

HOPE THIS HELPS!