18y^3-33y^2+2y+5 factor
Answers
Step-by-step explanation:
2y5-18y3
Final result :
2y3 • (y + 3) • (y - 3)
Step by step solution :
Step 1 :
Equation at the end of step 1 :
(2 • (y5)) - (2•32y3)
Step 2 :
Equation at the end of step 2 :
2y5 - (2•32y3)
Step 3 :
Step 4 :
Pulling out like terms :
4.1 Pull out like factors :
2y5 - 18y3 = 2y3 • (y2 - 9)
Trying to factor as a Difference of Squares :
4.2 Factoring: y2 - 9
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 : y2 is the square of y1
Factorization is : (y + 3) • (y - 3)
Final result :
2y3 • (y + 3) • (y - 3)