Question

add and subtract polynomials
2/8/2026 test
name: breyai
simplify each expression to its simplest form.

1. $(4x - 3) - (2x + 1)$

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

1. $(-6v^4 + 5v^3 - v) - (-5v^4 + 5v^4 - v)$

1. $(8 - 5k^2) - (7k^2 + 5)$

1. $2x^2 + 5x) + (7 + 5x^2 - x)$

Explanation:

Problem 1: \((4x - 3) - (2x + 1)\)

Step 1: Distribute the negative sign

To simplify the expression, we first distribute the negative sign to the terms inside the second parentheses. This gives us \(4x - 3 - 2x - 1\).

Step 2: Combine like terms

Next, we combine the like terms. The \(x\)-terms are \(4x\) and \(-2x\), and the constant terms are \(-3\) and \(-1\). Combining the \(x\)-terms: \(4x - 2x = 2x\). Combining the constant terms: \(-3 - 1 = -4\). So the simplified expression is \(2x - 4\).

Step 1: Remove the parentheses

Since we are adding the two polynomials, we can simply remove the parentheses: \(3x^3 + 5x - 4 + 5x^2 - 14x + 2\).

Step 2: Combine like terms

Now we combine the like terms. The \(x\)-terms are \(5x\) and \(-14x\), and the constant terms are \(-4\) and \(2\). The \(x^3\) and \(x^2\) terms have no like terms to combine with. Combining the \(x\)-terms: \(5x - 14x = -9x\). Combining the constant terms: \(-4 + 2 = -2\). So the simplified expression is \(3x^3 + 5x^2 - 9x - 2\).

Step 1: Simplify the second parentheses

First, we simplify the terms inside the second parentheses: \(-5v^4 + 5v^4 = 0\), so the second parentheses simplifies to \(0 - v = -v\). Now our expression is \(-6v^4 + 5v^3 - v - (-v)\).

Step 2: Distribute the negative sign

Distribute the negative sign to the \(-v\) inside the parentheses: \(-6v^4 + 5v^3 - v + v\).

Step 3: Combine like terms

The \(-v\) and \(+v\) cancel each other out (since \(-v + v = 0\)). So we are left with \(-6v^4 + 5v^3\).

Answer:

\(2x - 4\)

Problem 2: \((3x^3 + 5x - 4) + (5x^2 - 14x + 2)\)