Year 8 Maths: Simplifying Expressions

Introduction to Simplifying Expressions

Today, we’re going to learn about simplifying expressions. This is a very important skill in maths that helps us make complicated expressions easier to work with.

What is an Expression?

An expression is a combination of numbers, letters (which we call variables), and operations (like +, −, ×, and ÷). For example, the expression

Why Simplify Expressions?

Simplifying expressions makes them easier to understand and solve. It helps us to combine like terms and make our calculations quicker.

Key Rules for Simplifying Expressions

1. Like Terms

Like terms are terms that have the same variable and the same power. For example,

Example:

2. Constants

Constants are just numbers without variables. You can combine constants together too!

Example:

3. Combining Like Terms

When simplifying, always look for like terms! Add or subtract their coefficients (the numbers in front of the variables).

Example:

Tips for Simplifying Expressions

• Always look for like terms first.
• Keep your work neat to avoid mistakes.
• Check your answer by substituting values for the variables.

Examples of Simplifying Expressions

1. $$5x + 3x = 8x$$
2. $$7y – 2y + 4 = (7 – 2)y + 4 = 5y + 4$$
3. $$2a + 3b – 4a + 6b = (2 – 4)a + (3 + 6)b = -2a + 9b$$

Practice Questions

Easy Level Questions

1. Simplify: $$2x + 3x$$
2. Simplify: $$4y + 5y$$
3. Simplify: $$6 + 2$$
4. Simplify: $$5a + 2a$$
5. Simplify: $$3 + 7$$
6. Simplify: $$x + 4x$$
7. Simplify: $$8b – 3b$$
8. Simplify: $$10 + 5 – 3$$
9. Simplify: $$6p + 2p$$
10. Simplify: $$9 – 4 + 1$$

Medium Level Questions

1. Simplify: $$3x + 4y + 2x – y$$
2. Simplify: $$5a + 6b – 2a + 3b$$
3. Simplify: $$7m + 4 – 3m + 2$$
4. Simplify: $$8 – 2x + 5x + 7$$
5. Simplify: $$10k – 3 + 5k + 8$$
6. Simplify: $$4x + 7 – 2x + 9$$
7. Simplify: $$3x + 2y – x + 5y – 4$$
8. Simplify: $$2a – 3b + 5 – 2a + b$$
9. Simplify: $$6y + 9 – 4y + 2$$
10. Simplify: $$7 – 3x + 5x + 4$$

Hard Level Questions

1. Simplify: $$5x + 3y – 2x + 4y – y$$
2. Simplify: $$10a + 5 – 3a + 2b – 7 + 4b$$
3. Simplify: $$4x + 3y – 2x + 7 – 3y + x$$
4. Simplify: $$6a – 4b + 2a + 5b – 10 + 7$$
5. Simplify: $$2(x + 3) + 3(x – 4)$$
6. Simplify: $$3(p + 2) + 4(2p – 1)$$
7. Simplify: $$7x – 2(3x + 5) + x$$
8. Simplify: $$5(2y + 3) – 4(y – 2)$$
9. Simplify: $$3(2a – 4) + 2(3a + 1)$$
10. Simplify: $$8(x – 1) + 4(2x + 3) – 10$$

Answers

Easy Level Answers

1. $$5x$$
2. $$9y$$
3. $$8$$
4. $$7a$$
5. $$10$$
6. $$5x$$
7. $$5b$$
8. $$12$$
9. $$8p$$
10. $$6$$

Medium Level Answers

1. $$5x + 3y$$
2. $$3a + 9b$$
3. $$4m + 6$$
4. $$15 – 2x$$
5. $$15k + 5$$
6. $$2x + 16$$
7. $$2x + 7y – 4$$
8. $$-3b + 5$$
9. $$2y + 11$$
10. $$11 – 3x$$

Hard Level Answers

1. $$3x + 6y – 5$$
2. $$7a + 6b – 2$$
3. $$3x + 0y + 7$$
4. $$8a + b – 3$$
5. $$5x – 6$$
6. $$30p + 10$$
7. $$-5x – 10$$
8. $$10y + 7$$
9. $$9a – 10$$
10. $$12x + 2$$

Conclusion

Great job, Year 8! You’ve learned how to simplify expressions. Remember to practice regularly, and soon it will become second nature. If you have any questions, feel free to ask!