Simplification or other simple results

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This solution deals with simplification or other simple results.

Solution found

a*(2a+1)*(2a+5)

See steps

Step by Step Solution

Step 1 :

Equation at the end of step 1 :

  ((4 • (a³)) +  (2²•3a²)) +  5a
 Step  2  :

Equation at the end of step 2 :

  (2²a³ +  (2²•3a²)) +  5a

Step 3 :

Step 4 :

Pulling out like terms :

4.1 Pull out like factors :

4a³ + 12a² + 5a = a • (4a² + 12a + 5)

Trying to factor by splitting the middle term

4.2 Factoring 4a² + 12a + 5

The first term is, 4a² its coefficient is 4 .
The middle term is, +12a its coefficient is 12 .
The last term, "the constant", is +5

Step-1 : Multiply the coefficient of the first term by the constant 4 • 5 = 20

Step-2 : Find two factors of 20 whose sum equals the coefficient of the middle term, which is 12 .

-20	+	-1	=	-21
-10	+	-2	=	-12
-5	+	-4	=	-9
-4	+	-5	=	-9
-2	+	-10	=	-12
-1	+	-20	=	-21
1	+	20	=	21
2	+	10	=	12	That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 2 and 10
                     4a² + 2a + 10a + 5

Step-4 : Add up the first 2 terms, pulling out like factors :
                    2a • (2a+1)
              Add up the last 2 terms, pulling out common factors :
                    5 • (2a+1)
Step-5 : Add up the four terms of step 4 :
                    (2a+5)  •  (2a+1)
             Which is the desired factorization

Final result :

  a • (2a + 1) • (2a + 5)

Terms and topics

Canceling out