Question

distribute a negative 1 if there is a negative in fro

1. $(5 - 3x^4) - (3 + x^4)$
2. $(r^4 - 4r^2) - (5r^2 + 2r^4)$
3. $(3v + 14v^5) - (14v + 11v^4 + 5v^5)$

Explanation:

Problem 26: \((5 - 3x^4) - (3 + x^4)\)

Step 1: Distribute the negative sign

We need to distribute the negative sign to the terms inside the second parentheses. So, \((5 - 3x^4) - (3 + x^4)=5 - 3x^4 - 3 - x^4\)

Step 2: Combine like terms

First, combine the constant terms: \(5 - 3 = 2\). Then, combine the \(x^4\) terms: \(-3x^4 - x^4=-4x^4\). So, putting it together, we get \(2 - 4x^4\)

Step 1: Distribute the negative sign

Distribute the negative sign to the terms inside the second parentheses: \((r^4 - 4r^2) - (5r^2 + 2r^4)=r^4 - 4r^2 - 5r^2 - 2r^4\)

Step 2: Combine like terms

Combine the \(r^4\) terms: \(r^4- 2r^4=-r^4\). Combine the \(r^2\) terms: \(-4r^2- 5r^2=-9r^2\). So, the result is \(-r^4 - 9r^2\)

Step 1: Distribute the negative sign

Distribute the negative sign to the terms inside the second parentheses: \((3v + 14v^5) - (14v + 11v^4 + 5v^5)=3v + 14v^5 - 14v - 11v^4 - 5v^5\)

Step 2: Combine like terms

Combine the \(v\) terms: \(3v-14v = - 11v\). Combine the \(v^5\) terms: \(14v^5-5v^5 = 9v^5\). The \(v^4\) term remains as \(-11v^4\). So, the result is \(9v^5-11v^4 - 11v\)

Answer:

\(2 - 4x^4\)

Problem 28: \((r^4 - 4r^2) - (5r^2 + 2r^4)\)