Answer: 25a^6cm^25 - a^2b^2cm^25 - b
- STEP 1
:
Equation at the end of step 1
((((5^2a^4 - b^2) • c) • m^25) • a^2) - b
- STEP 2
:
Trying to factor as a Difference of Squares:
2.1 Factoring: 25a^4-b^2
Theory : A difference of two perfect squares, A^2 - B^2 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 : 25 is the square of 5
Check : a4 is the square of a2
Check : b2 is the square of b1
Factorization is : (5a^2 + b) • (5a^2 - b)
-
Trying to factor as a Difference of Squares:
2.2 Factoring: 5a^2 - b
Check : 5 is not a square !!
Ruling : Binomial can not be factored as the
difference of two perfect squares
- Equation at the end of step 2
:
((c•(5a^2+b)•(5a^2-b)•m^25)•a^2)-b
- STEP 3
:
Equation at the end of step 3
(cm^25 • (5a^2 + b) • (5a^2 - b) • a^2) - b
- STEP 4:
Equation at the end of step 4
a^2cm^25 • (5a^2 + b) • (5a^2 - b) - b
- STEP 5
:
Trying to factor a multi variable polynomial
5.1 Factoring 25a^6cm^25 - a^2b^2cm^25 - b
Try to factor this multi-variable trinomial using trial and error
Final result :
25a^6cm^25 - a^2b^2cm^25 - b
Step-by-step explanation:
Hope it helps out!
