FORM 2 • TERM 1 • LESSON 09

In the last lesson you wrote and evaluated expressions. Now you will learn to simplify them – write them in the shortest possible way. You will name the parts of an expression, model terms with algebra tiles, multiply and divide terms, and collect like terms. This builds on the Form 1 lesson on simplifying expressions and like terms.

Learning outcomes

By the end of this lesson you should be able to:

• 2.6.2.1 – Explain what an algebraic expression is.
• 2.6.2.2 – Show terms with objects (algebra tiles), pictures and symbols.
• 2.6.2.3 – Identify like and unlike terms.
• 2.6.2.4 – Tell the difference between a coefficient and an operational sign.
• 2.6.2.5 – Add, subtract, multiply and divide terms using tiles, pictures and symbols.
• 2.6.2.6 – Simplify algebraic expressions.

What is an algebraic expression?

An algebraic expression is a collection of numbers and letters joined by operations, such as 4x − 3y + 7. It has no equals sign, so it cannot be “solved” – but it can be simplified, and it can be evaluated if you know the letters.

• A term is one part of the expression: 4x, 3y and 7 are the three terms of 4x − 3y + 7.
• A coefficient is the number multiplying a letter: in 4x the coefficient of x is 4. In x on its own, the coefficient is 1.
• A constant is a term with no letter, such as 7.
• An operational sign is the + or − written between terms. It tells you whether to add or subtract the next term.

Coefficient or operational sign?

In 4x − 3y + 7, the coefficient of y is 3, and the operational sign in front of it is −. The sign is not part of the coefficient when you name it, but it always travels with the term after it when you rearrange or collect terms. So the term is really “−3y”, and you can write the expression as 4x + 7 − 3y, but not as 4x + 3y − 7.

Algebra tiles

Algebra tiles are a concrete way to see terms. A long tile stands for x, a small square stands for 1, and a large square stands for x². Shaded (orange) tiles are negative.

A positive tile and its negative tile make a zero pair, because x + (−x) = 0 and 1 + (−1) = 0. Taking out zero pairs is how tiles show adding and subtracting:

Like and unlike terms

Like terms have exactly the same letters, with the same powers. Only like terms can be added or subtracted into a single term.

Like terms	Unlike terms
3x and −5x	3x and 3y
2ab and 7ba (ab = ba)	4a and 4a²
x² and −6x²	5 and 5x

To collect like terms, add or subtract the coefficients and keep the letters: 5a + 3b − 2a + b = (5 − 2)a + (3 + 1)b = 3a + 4b.

Multiplying and dividing terms

You can multiply or divide any terms, like or unlike. Multiply (or divide) the numbers, then the letters.

• 3 × 2x = 6x (three groups of 2x tiles is 6x tiles).
• 2a × 3b = 6ab.
• x × x = x², and 4x × 5x = 20x².
• 12x ÷ 4 = 3x.
• 10ab ÷ 5a = 2b.
• −6y × 2 = −12y, using the integer sign rules.

Worked examples

Example 1: Naming the parts

Question: For 6m − 4n + 9, write down
(a) the terms
(b) the coefficient of n
(c) the operational sign before the n-term
(d) the constant.

1. (a) The parts separated by + and − are 6m, 4n and 9 (the n-term is −4n).
2. (b) The number multiplying n is 4.
3. (c) The sign in front of it is −.
4. (d) The term with no letter is 9.

Answer:
(a) 6m, −4n, 9
(b) 4
(c) −
(d) 9.

Example 2: Like terms

Question: From 4p, −2q, p², 7p, 3qp, −pq, 5, pick out the groups of like terms.

1. 4p and 7p have only p.
2. 3qp and −pq both have p × q.
3. −2q, p² and 5 have no partners.

Answer: 4p and 7p; 3qp and −pq.

Example 3: Collecting like terms

Question: Simplify 7p − 3q − 9p + 8q.

1. Gather the p-terms: 7p − 9p = −2p.
2. Gather the q-terms: −3q + 8q = 5q.

Answer: −2p + 5q (or 5q − 2p).

Example 4: Terms with squares

Question: Simplify 4x² + 3x − x² − 5x + 2.

1. x²-terms: 4x² − x² = 3x².
2. x-terms: 3x − 5x = −2x.
3. The constant 2 has no partner.

Answer: 3x² − 2x + 2.

Example 5: Multiplying and dividing

Question: Simplify
(a) 4a × 3b
(b) −5x × 2x
(c) 18pq ÷ 6q.

1. (a) 4 × 3 = 12 and a × b = ab.
2. (b) −5 × 2 = −10 and x × x = x².
3. (c) 18 ÷ 6 = 3 and pq ÷ q = p.

Answer:
(a) 12ab
(b) −10x²
(c) 3p.

Example 6: Using tiles

Question: Use tiles to simplify (3x − 2) + (−x + 5).

1. Lay out 3 x-tiles and 2 negative unit tiles, then 1 negative x-tile and 5 unit tiles.
2. Remove zero pairs: one x with one −x, and two 1s with two −1s.
3. Left: 2 x-tiles and 3 unit tiles.

Answer: 2x + 3.

Common mistakes

• Adding unlike terms. 3x + 2y cannot be simplified; it is not 5xy.
• Losing the sign. In 8a − 3b + 2b, the −3b keeps its minus: the answer is 8a − b, not 8a + 5b.
• Mixing up x² and 2x. x × x = x², but x + x = 2x.
• Forgetting the hidden 1. x means 1x, so 5x − x = 4x, not 5.
• Treating x and x² as like terms. 4x + 3x² stays as it is.

Practice questions

Try these yourself first, then open each answer to check your working.

Quick check

Previous: Algebra Review: Variables, Word Statements and Substituting Integers

Next: Linear Equations: Letters on Both Sides, Brackets and Word Problems

Curriculum link: This post is relevant to the Trinidad and Tobago National Lower Secondary (NCSE) Mathematics Curriculum – Form 2, Term 1, Strand 2.6 Algebra, Topic 2.6.2 Simplification of Algebraic Expressions – Learning Outcomes 2.6.2.1 (algebraic expressions), 2.6.2.2 (representing terms concretely, pictorially and symbolically), 2.6.2.3 (like and unlike terms), 2.6.2.4 (coefficient and operational sign), 2.6.2.5 (operations on terms) and 2.6.2.6 (simplifying algebraic expressions).

Updates

2026/10/23

– First version of this lesson.

2026/10/25

– Put each lettered part of the questions and answers on its own line.

© 2026 Vedesh Kungebeharry. All rights reserved.