What is factor 1+343n^3 ?

The solution to factor 1+343n^3 is (7n+1)(49n^2-7n+1)

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factor 1+343n^3

factor

1 + 343 n^{3}

(7 n + 1) (49 n^{2} - 7 n + 1)

Solution steps

1 + 343 n^{3}

Write in the standard form

= 343 n^{3} + 1

Apply exponent rules

= (7 n)^{3} + 1^{3}

Apply Sum of Cubes Formula:

x^{3} + y^{3} = (x + y) (x^{2} - x y + y^{2})

(7 n)^{3} + 1^{3} = (7 n + 1) (7^{2} n^{2} - 7 n + 1)

= (7 n + 1) (7^{2} n^{2} - 7 n + 1)

7^{2} = 49

= (7 n + 1) (49 n^{2} - 7 n + 1)

65 (\frac{5}{7}) - 36

2 \cdot 2^{x}

8 r^{3} - 64 r^{2} + r - 8

3 a + 3 b

4 - (+ 9) - (- 28) + 19