Question

question
combine like terms
y + x + 3x² + 8x
answer:
3x

Explanation:

Step1: Identify like terms

In the expression \( y + x + 3x^2 + 8x \), the like terms are \( x \) and \( 8x \) (both are linear terms in \( x \)), \( y \) is a term in \( y \), and \( 3x^2 \) is a quadratic term in \( x \).

Step2: Combine like terms

Combine \( x \) and \( 8x \): \( x + 8x = 9x \). The other terms \( y \) and \( 3x^2 \) have no like terms to combine with, so they remain as is. So the combined expression is \( 3x^2 + 9x + y \). Wait, but the initial wrong answer was \( 3x \), let's re - check. Wait, maybe I misread the original expression. Wait, the original expression is \( y + x + 3x^2 + 8x \)? Wait, no, maybe it's a typo? Wait, if the expression is \( y + x + 3x + 8x \)? No, the user's image shows \( y + x + 3x^2 + 8x \)? Wait, no, maybe the original expression is \( y + x + 3x + 8x \)? Wait, no, the user's problem is to combine like terms for \( y + x + 3x^2 + 8x \). Wait, but the wrong answer was \( 3x \). Wait, maybe the expression is \( y + x + 3x + 8x \)? No, let's do it correctly.

Wait, let's take the expression as given: \( y + x + 3x^2 + 8x \). Like terms for \( x \): \( x+8x = 9x \). So the combined expression is \( 3x^2+9x + y \). But if the expression was supposed to be \( y + x + 3x + 8x \) (without the \( x^2 \) term), then \( x + 3x+8x=12x \), plus \( y \). But the user's input has \( 3x^2 \). Wait, maybe the original problem was \( y + x + 3x + 8x \)? No, the image shows \( 3x^2 \). Wait, maybe the user made a typo, but according to the standard way of combining like terms:

For the expression \( y + x + 3x^2 + 8x \):

• Terms: \( y \) (degree 0 in \( x \), variable \( y \)), \( x \) (degree 1 in \( x \)), \( 3x^2 \) (degree 2 in \( x \)), \( 8x \) (degree 1 in \( x \)).

• Combine degree 1 terms: \( x + 8x=9x \).

• So the simplified expression is \( 3x^2 + 9x + y \).

But if the expression was \( y + x + 3x + 8x \) (assuming \( 3x^2 \) is a typo for \( 3x \)), then \( x + 3x + 8x=12x \), plus \( y \). But the wrong answer was \( 3x \), which is incorrect.

Wait, maybe the original expression is \( y + x + 3x^2 + 8x \), and the user's wrong answer was \( 3x \), but the correct way is:

1. Identify like terms: \( x \) and \( 8x \) are like terms (same variable, same exponent).

1. Combine them: \( x+8x = 9x \).

1. The other terms \( 3x^2 \) (quadratic in \( x \)) and \( y \) (linear in \( y \)) have no like terms, so the combined expression is \( 3x^2+9x + y \).

But if the problem was to combine \( x + 8x+3x \) (maybe a miswritten expression), then \( x + 8x+3x=(1 + 8+3)x = 12x \). But the given wrong answer is \( 3x \), which is incorrect.

Wait, maybe the original expression is \( y + x + 3x + 8x \), and the user made a typo with \( 3x^2 \). Let's assume that the expression is \( y + x + 3x + 8x \) (removing the square by mistake). Then:

Step1: Identify like terms

The like terms are \( x \), \( 3x \), and \( 8x \) (all are linear terms in \( x \)), and \( y \) is a separate term.

Step2: Combine like terms

\( x+3x + 8x=(1 + 3+8)x=12x \). So the combined expression is \( 12x + y \). But the wrong answer was \( 3x \), which is still incorrect.

Wait, maybe the expression is \( y + x + 3x^2+8x \), and the user's wrong answer was a mistake. Let's do it correctly for the given expression \( y + x + 3x^2 + 8x \):

• Combine \( x \) and \( 8x \): \( x + 8x=9x \).

• The expression becomes \( 3x^2+9x + y \).

Answer:

\( 3x^2 + 9x + y \) (If the expression was \( y + x + 3x + 8x \), the answer would be \( 12x + y \), but based on the given \( 3x^2 \) term, the correct combined form is \( 3x^2+9x + y \))