Question

What is the factored of 7gh⁴ - 14 gh²​

Answer 1

Answer:

7gh2 x (h2 - 2)

Step-by-step explanation:

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "h2"   was replaced by   "h^2".  1 more similar replacement(s).

STEP 1

(7g x (h^4)) -  (2x7gh^2)

STEP  2

Equation at the end of step 2

7gh^4 -  (2x7gh^2)

STEP 3

Pull out like factors

7gh^4 - 14gh^2  =   7gh^2 x (h^2 - 2)

Trying Factoring:  h2 - 2  

Theory: A difference of two perfect squares,  A^2 - B^2  can be factored into  (A+B) • (A-B)

factor as a Difference of Squares:

Proof :  (A+B) • (A-B) =

        A^2 - AB + BA - B^2 =

        A^2 - AB + AB - B^2 =

        A^2 - B^2

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

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

Check : 2 is not a square !!

Final result :

7gh2 x (h2 - 2)