%5E3-7n(n%5E2-2).jpeg "(1-2n)^3-7n(n^2-2)")
Simplifying the Expression (1-2n)^3 - 7n(n^2-2)
This article will explore the process of simplifying the expression (1-2n)^3 - 7n(n^2-2).
Expanding the Expression
First, we expand the cube of the binomial using the formula (a-b)^3 = a^3 - 3a^2b + 3ab^2 - b^3:
(1-2n)^3 = 1^3 - 3(1^2)(2n) + 3(1)(2n)^2 - (2n)^3
Simplifying this, we get:
(1-2n)^3 = 1 - 6n + 12n^2 - 8n^3
Now, we expand the second term:
7n(n^2-2) = 7n^3 - 14n
Combining Terms
Finally, we combine the expanded terms:
(1-2n)^3 - 7n(n^2-2) = (1 - 6n + 12n^2 - 8n^3) - (7n^3 - 14n)
Combining like terms, we get:
-15n^3 + 12n^2 + 8n + 1
Therefore, the simplified form of the expression (1-2n)^3 - 7n(n^2-2) is -15n^3 + 12n^2 + 8n + 1.
This expression can be useful in various mathematical contexts, such as solving equations or analyzing functions.