factorization:
9y^2+81y+y+9
Answers
Answer:
HOLA MATE, HERE IS UR ANSWER :
Step-by-step explanation:
9y^2+81y+y+9
=>9y(y+9)+1(y+9)
=>(y+9) (9y+1).ANS
:) :) HOPE ITS HELP YOU
Answer:
Step-by-step explanation:
((9 • (y3)) + 34y2) - y) - 9
STEP
2
:
Equation at the end of step
2
:
((32y3 + 34y2) - y) - 9
STEP
3
:
Checking for a perfect cube
3.1 9y3+81y2-y-9 is not a perfect cube
Trying to factor by pulling out :
3.2 Factoring: 9y3+81y2-y-9
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: -y-9
Group 2: 9y3+81y2
Pull out from each group separately :
Group 1: (y+9) • (-1)
Group 2: (y+9) • (9y2)
-------------------
Add up the two groups :
(y+9) • (9y2-1)
Which is the desired factorization
Trying to factor as a Difference of Squares:
3.3 Factoring: 9y2-1
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 : 1 is the square of 1
Check : y2 is the square of y1
Factorization is : (3y + 1) • (3y - 1)
Final result :
(3y + 1) • (3y - 1) • (y + 9) Hope it helps