Mathematics • Year 7 • Unit 2 • Lesson 6

Multiplying Algebraic Terms

Build the basics: multiply coefficients separately, multiply variables separately, add powers when the same letter appears twice, and handle negative signs cleanly.

Build · I Do / We Do / You Do

1. I do — fully worked example

Read every line. Each step has a short reason on the right so you can see why, not just what.

Problem. Simplify 3x × 4y.

Step 1 — Split into coefficients and variables.

3x × 4y = (3 × 4) × (x × y)

Reason: multiplication is commutative — we can rearrange so the numbers sit together and the letters sit together.

Step 2 — Multiply the coefficients.

3 × 4 = 12

Reason: just the numbers — basic multiplication.

Step 3 — Multiply the variables.

x × y = xy

Reason: two different letters just sit next to each other (no × sign needed). Write them in alphabetical order.

Step 4 — Put coefficient and variables together.

12 × xy = 12xy

Reason: coefficient always goes in front of the variables.

Answer: 3x × 4y = 12xy.

Stuck? Revisit lesson § "The Big Idea" — multiply the coefficients, then multiply the variables, then write them together.

2. We do — fill in the missing steps

Same structure as Section 1, but with the working faded. Fill in each blank line. 4 marks

Problem. Simplify 2a × 5a.

Step 1 — Group coefficients and variables:

2a × 5a = (____ × ____) × (____ × ____)

Step 2 — Multiply the coefficients:

____ × ____ = ______

Step 3 — Multiply the variables (same letter twice → power goes up):

a × a = a^____

Step 4 — Combine:

Final answer = ____________

Stuck? Revisit lesson § "Same Variable: Add Powers" — a × a = a², not 2a.

3. You do — independent practice

Show your working under each question. The first four are foundation, the middle two are standard, and the last two are extension.

Foundation — single step

3.1 Simplify 2x × 3y. 1 mark

3.2 Simplify 4a × 5. 1 mark

3.3 Simplify x × x. 1 mark

3.4 Simplify 6m × 2n. 1 mark

Standard — combine two ideas

3.5 Simplify 3x × 5x. (Hint: same letter twice.) 2 marks

3.6 Simplify (−4a)(2b). 2 marks

Extension — push your thinking

3.7 Simplify 2a × 3b × 4a. Write the variables in alphabetical order. 3 marks

3.8 Simplify (−2x)(3xy)(−y). Be careful with signs and watch the y appearing twice. 3 marks

Stuck on 3.8? Count the negatives. Two negatives multiplied = positive. Then handle each variable separately.

How did this worksheet feel?

Got it Partly Lost

What I'll revisit before next class:

Answers — Do not peek before attempting

Section 2 — We do (2a × 5a)

Step 1: 2a × 5a = (2 × 5) × (a × a).
Step 2: 2 × 5 = 10.
Step 3: a × a = a² (one a multiplied by another a is "a-squared", not 2a).
Step 4: Final answer = 10a².

3.1 — 2x × 3y

Coefficients: 2 × 3 = 6. Variables: x × y = xy. Answer: 6xy.

3.2 — 4a × 5

Coefficients: 4 × 5 = 20. Variable: a (only one variable here). Answer: 20a.

3.3 — x × x

Same letter twice — add the powers. x × x = x¹⁺¹ = x². (Not 2x — that would be x + x.)

3.4 — 6m × 2n

Coefficients: 6 × 2 = 12. Variables: m × n = mn. Answer: 12mn.

3.5 — 3x × 5x

Coefficients: 3 × 5 = 15. Variables: x × x = x². Answer: 15x². (Both the coefficient AND the power go up.)

3.6 — (−4a)(2b)

Coefficients: −4 × 2 = −8 (neg × pos = neg). Variables: a × b = ab. Answer: −8ab.

3.7 — 2a × 3b × 4a

Coefficients: 2 × 3 × 4 = 24. Variables: a × b × a = a² × b = a²b. Answer: 24a²b. (Two a's → a²; the single b stays as b; alphabetical order so a before b.)

3.8 — (−2x)(3xy)(−y)

Coefficients: (−2) × 3 × (−1) = +6 (two negatives cancel out). Variables: x × xy × y = x² × y² = x²y² (two x's give x², two y's give y²). Answer: 6x²y².