https://file.aiquickdraw.com/mathbot/file/1729510578008avwov95t.jpg

Let's solve the questions in **Q1** from the image. The task is to **remove the brackets and simplify** where possible.

### 1. (a) \( 2x(x - 2) \)
Expand:
\[
2x(x - 2) = 2x^2 - 4x
\]

### 1. (b) \( (y - 3)x \)
Distribute \( x \) across the terms inside the parentheses:
\[
(y - 3)x = yx - 3x
\]

### 1. (c) \( (x - 2) - 3x \)
Expand:
\[
(x - 2) - 3x = x - 2 - 3x = -2x - 2
\]

### 1. (d) \( -2x - (x - 2) \)
Distribute the negative sign:
\[
-2x - (x - 2) = -2x - x + 2 = -3x + 2
\]

### 1. (e) \( (x - 3)(-2x) \)
Expand:
\[
(x - 3)(-2x) = -2x^2 + 6x
\]

### 1. (f) \( 2(x + 1) - (1 - x) \)
Distribute and simplify:
\[
2(x + 1) - (1 - x) = 2x + 2 - 1 + x = 3x + 1
\]

### 1. (g) \( x(x^2 - 2x - 1) \)
Distribute \( x \):
\[
x(x^2 - 2x - 1) = x^3 - 2x^2 - x
\]

### 1. (h) \( -x(1 - x) + 2(x + 3) - 4 \)
Expand each part:
\[
-x(1 - x) = -x + x^2
\]
\[
2(x + 3) = 2x + 6
\]
Now simplify the entire expression:
\[
-x + x^2 + 2x + 6 - 4 = x^2 + x + 2
\]

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If you'd like, I can move on to question 2 or explain any of the solutions in more detail!

### 5 Related Questions:
1. How do you expand expressions involving both constants and variables?
2. What are the rules for distributing negative signs?
3. How do you simplify expressions after expanding?
4. How can you factor expressions after expansion?
5. How do we approach multi-term polynomial distribution?

### Tip:
Always expand step by step and be careful when distributing negative signs to avoid errors in simplification.

Remove the brackets and simplify where possible for the algebraic expressions in Q1.

Learn how to remove brackets and simplify algebraic expressions using the distributive property. This example focuses on expanding expressions, distributing signs, and combining like terms. Ideal for students in Grades 7-9.

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