https://r2.erweima.ai/mathbot/image/17258504299252bsykczi.jpg

Let's go through the simplification of each part from the photo you provided:

**a.** \( 12x - 3y + 17x - x + y \)

**b.** \( 21xy + 4x - 3y + 14xy - x + y + xy \)

**c.** \( 4u - 3v + u - 3v - u - 4u \)

**d.** \( y - x^2 + y + 3xy - 12xy - y - y + 14x^2 - 2xy \)

Let's start by combining like terms for each expression.

**a.** Combine the terms involving \( x \) and \( y \):

\[ 12x - 3y + 17x - x + y = (12x + 17x - x) + (-3y + y) = 28x - 2y \]

**b.** Combine the terms involving \( xy \), \( x \), and \( y \):

\[ 21xy + 4x - 3y + 14xy - x + y + xy = (21xy + 14xy + xy) + (4x - x) + (-3y + y) = 36xy + 3x - 2y \]

**c.** Combine the terms involving \( u \) and \( v \):

\[ 4u - 3v + u - 3v - u - 4u = (4u + u - u - 4u) + (-3v - 3v) = -6v \]

**d.** Combine the terms involving \( x^2 \), \( xy \), and \( y \):

\[ y - x^2 + y + 3xy - 12xy - y - y + 14x^2 - 2xy = (-x^2 + 14x^2) + (3xy - 12xy - 2xy) + (y + y - y - y) = 13x^2 - 11xy \]

Here are the simplified expressions:
- **a.** \( 28x - 2y \)
- **b.** \( 36xy + 3x - 2y \)
- **c.** \( -6v \)
- **d.** \( 13x^2 - 11xy \)

Would you like to go into more detail on any of these problems, or do you have any other questions?

**Further Questions:**
1. How do you determine which terms are like terms?
2. What are the rules for combining like terms?
3. Can you explain why \( x^2 \) and \( xy \) are not combined in part d?
4. What would be the next steps if you had to use these simplified expressions in an equation?
5. How can you factor an expression like \( 13x^2 - 11xy \)?

**Tip:** When simplifying algebraic expressions, always organize your work by grouping like terms to avoid missing any and ensure accuracy.

Simplify the following expressions:
 a) 12x - 3y + 17x - x + y
 b) 21xy + 4x - 3y + 14xy - x + y + xy
 c) 4u - 3v + u - 3v - u - 4u
 d) y - x^2 + y + 3xy - 12xy - y - y + 14x^2 - 2xy

Learn how to simplify algebraic expressions such as 12x - 3y + 17x - x + y and 21xy + 4x - 3y + 14xy. This guide provides step-by-step solutions, explaining how to combine like terms and simplify expressions. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation