Question

simplify each expression.

1. $(4n^4 - 5 + 7n^2) - (1 + 2n^2 + 8n^4)$
2. $(3v - 5 + 6v^4) - (8v^4 + 5 + 3v)$

Explanation:

Step1: Simplify the first expression \((4n^4 - 5 + 7n^2)-(1 + 2n^2 + 8n^4)\)

First, remove the parentheses: \(4n^4 - 5 + 7n^2 - 1 - 2n^2 - 8n^4\)
Then, combine like terms:
For \(n^4\) terms: \(4n^4-8n^4=-4n^4\)
For \(n^2\) terms: \(7n^2 - 2n^2 = 5n^2\)
For constant terms: \(-5-1=-6\)
So the simplified form is \(-4n^4 + 5n^2 - 6\)

Step2: Simplify the second expression \((3v - 5 + 6v^4)-(8v^4 + 5 + 3v)\)

First, remove the parentheses: \(3v - 5 + 6v^4 - 8v^4 - 5 - 3v\)
Then, combine like terms:
For \(v^4\) terms: \(6v^4-8v^4=-2v^4\)
For \(v\) terms: \(3v - 3v = 0\)
For constant terms: \(-5-5=-10\)
So the simplified form is \(-2v^4 - 10\)

Answer:

First expression: \(\boldsymbol{-4n^4 + 5n^2 - 6}\)
Second expression: \(\boldsymbol{-2v^4 - 10}\)