Answer:
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "q2" was replaced by "q^2". 1 more similar replacement(s).
STEP
1
:
Equation at the end of step 1
(9 • (p2)) - (23•5q2)
STEP
2
:
Equation at the end of step
2
:
32p2 - (23•5q2)
STEP
3
:
Trying to factor as a Difference of Squares:
3.1 Factoring: 9p2-40q2
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 : 9 is the square of 3
Check : 40 is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares.