Questions: Perform the indicated operation by removing the parentheses and combining like terms. (5x^2 + 3x) + (x^2 - 8x + 4)

Transcript text: Perform the indicated operation by removing the parentheses and combining like terms. \[ \left(5 x^{2}+3 x\right)+\left(x^{2}-8 x+4\right) \]

Solution

Solution Steps

To solve this problem, we need to remove the parentheses and then combine like terms. Specifically, we will add the coefficients of the \(x^2\) terms together, the coefficients of the \(x\) terms together, and the constant terms together.

Step 1: Remove Parentheses

We start with the expression: \[ (5x^2 + 3x) + (x^2 - 8x + 4) \] Removing the parentheses, we rewrite it as: \[ 5x^2 + 3x + x^2 - 8x + 4 \]

Step 2: Combine Like Terms

Next, we combine the like terms. For the \(x^2\) terms: \[ 5x^2 + x^2 = 6x^2 \] For the \(x\) terms: \[ 3x - 8x = -5x \] And the constant term remains: \[ 4 \]

Step 3: Write the Final Expression

Combining all the results, we have: \[ 6x^2 - 5x + 4 \]