Answer:
STEP1:Equation at the end of step 1
2y3 - 8y
STEP2:
STEP3:Pulling out like terms
3.1 Pull out like factors :
2y3 - 8y = 2y • (y2 - 4)
Trying to factor as a Difference of Squares:
3.2 Factoring: y2 - 4
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 : 4 is the square of 2
Check : y2 is the square of y1
Factorization is : (y + 2) • (y - 2)
Final result :
2y • (y + 2) • (y - 2)
