Factor completely.

16n^6+40n^3+25

Answer:Step 1:

Equation at the end of step 1:

((16 • (n6)) + (23•5n3)) + 25

Step 2:

Equation at the end of step 2:

(24n6 + (23•5n3)) + 25

Step 3:

Trying to factor by splitting the middle term

3.1 Factoring 16n6+40n3+25

The first term is, 16n6 its coefficient is 16.

The middle term is, + 40n3 its coefficient is 40.

The last term, "the constant", is + 25

Step-1 : Multiply the coefficient of the first term by the constant 16 • 25 = 400

Step-2 : Find two factors of 400 whose sum equals the coefficient of the middle term, which is 40.

-400 + - 1 = - 401

-200 + - 2 = - 202

-100 + - 4 = - 104

-80 + - 5 = - 85

-50 + - 8 = - 58

-40 + - 10 = - 50

-25 + - 16 = - 41

-20 + - 20 = - 40

-16 + - 25 = - 41

-10 + - 40 = - 50

-8 + - 50 = - 58

-5 + - 80 = - 85

-4 + - 100 = - 104

-2 + - 200 = - 202

-1 + - 400 = - 401

1 + 400 = 401

2 + 200 = 202

4 + 100 = 104

5 + 80 = 85

8 + 50 = 58

10 + 40 = 50

16 + 25 = 41

20 + 20 = 40 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 20 and 20

16n6 + 20n3 + 20n3 + 25

Step-4 : Add up the first 2 terms, pulling out like factors:

4n3 • (4n3+5)

Add up the last 2 terms, pulling out common factors:

5 • (4n3+5)

Step-5 : Add up the four terms of step 4:

(4n3+5) • (4n3+5)

Which is the desired factorization

Trying to factor as a Sum of Cubes:

3.2 Factoring: 4n3+5

Theory : A sum of two perfect cubes, a3 + b3 can be factored into:

(a+b) • (a2-ab+b2)

Proof : (a+b) • (a2-ab+b2) =

a3-a2b+ab2+ba2-b2a+b3 =

a3 + (a2b-ba2) + (ab2-b2a) + b3=

a3+0+0+b3=

a3+b3

Check : 4 is not a cube!

Step-by-step explanation: I believe that is the answer because i got it right.

Step-by-step explanation:

(a + b) ² = a² + 2ab + b²

16n⁶ + 40n³ + 25 = 4² * (n³) ² + 2 * 4n³ * 5 + 5²

= (4n³) ² + 2 * 4n³*5 + 5²

= (4n³ + 5) ²