50 - 2y2
STEP
2
:
STEP
3
:
Pulling out like terms
3.1 Pull out like factors :
50 - 2y2 = -2 • (y2 - 25)
Trying to factor as a Difference of Squares:
3.2 Factoring: y2 - 25
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 : 25 is the square of 5
Check : y2 is the square of y1
Factorization is : (y + 5) • (y - 5)
Final result :
-2 • (y + 5) • (y - 5)
