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.