Lesson title: Multiplying terms

Do Now

Copy then answer:

Simplify these expressions:

  1. \(4a + 3a\)

  2. \(8x - 5x\)

  3. \(2m + m\)

  1. \(7p - 2p - p\)

  2. \(3n + 4n + n\)

  3. \(10b - b\)

Quick check - Study this working

Ahmed’s (correct) working: \[\begin{align*} 5x + 2x &= 7x\\ \end{align*}\]

Answer these questions:

  1. Explain what Ahmed did here?
  2. Now simplify: \(6y + 3y\)

Today’s learning

By the end of this lesson, you will be able to:

  • Multiply terms correctly
  • Understand the difference between adding and multiplying terms
  • Write your working clearly

Key vocabulary

Copy these definitions:

Coefficient: The number in front of a variable

  • In \(5x\), the coefficient is 5

Term: A number, variable, or combination connected by multiplication

  • Examples: \(3\), \(x\), \(4a\), \(2xy\)

Adding/subtracting vs multiplying

Copy this important difference:

Adding like terms: \(3x + 2x = 5x\) (add the coefficients)

Multiplying terms: \(3 \times 2x = 6x\) (multiply the number by the coefficient)

Key: When we multiply, we multiply ALL the numbers (including pronumerals) together

Multiplying a number by a term

Copy these examples:

Expression Working Answer
\(4 \times 3a\) \(4 \times 3 \times a\) \(12a\)
\(2 \times 5x\) \(2 \times 5 \times x\) \(10x\)
\(6m \times 3\) \(6 \times m \times 3\) \(18m\)

Your turn

Copy and complete:

  1. \(5 \times 2b = ?\)

  2. \(3 \times 4n = ?\)

  3. \(7p \times 2 = ?\)

  1. \(6 \times 3x = ?\)

  2. \(4a \times 5 = ?\)

  3. \(8 \times 2m = ?\)

Complete the working

Copy and fill in the missing steps:

Example: \(3 \times 7x\)

\[\begin{align*} 3 \times 7x &= 3 \times 7 \times x \\ &= \underline{\hspace{1cm}} \times x \\ &= \underline{\hspace{1cm}} \end{align*}\]

Now complete: \(4 \times 5y\)

\[\begin{align*} 4 \times 5y &= \underline{\hspace{3cm}} \\ &= \underline{\hspace{1cm}} \times y \\ &= \underline{\hspace{1cm}} \end{align*}\]

Multiplying a term by a term

Copy this new rule:

Example 1:

\[x \times x = x^2\]

Example 2 (including coefficients):

\[\begin{align*} 2x \times 3x &= 2 \times x \times 3 \times x \\ &= 2 \times 3 \times x \times x \\ &= 6 \times x^2 \\ &= 6x^2 \end{align*}\]

Study this solution

Bella’s working for \(4a \times 5a\):

\[\begin{align*} 4a \times 5a &= 4 \times a \times 5 \times a \\ &= 4 \times 5 \times a \times a \\ &= 20 \times a^2 \\ &= 20a^2 \end{align*}\]

Answer:

  1. What happened to the coefficients 4 and 5?
  2. What happened to the variables \(a\) and \(a\)?
  3. Now you try: \(3b \times 2b\)

Practice - Term × Term

Complete these with full working:

\(2m \times 4m\)

\(5x \times 3x\)

\(6p \times 2p\)

Common mistakes

Which is correct? Circle the right answer:

\(3x \times 2x = ?\)

  1. \(5x\)

  2. \(6x\)

  3. \(6x^2\)

\(4 \times 5a = ?\)

  1. \(9a\)

  2. \(20a\)

  3. \(20\)

\(m \times m = ?\)

  1. \(2m\)

  2. \(m^2\)

  3. \(m\)

Find and fix the error

Find the mistake and write the correct solution:

Charlie’s working: \[\begin{align*} 3x \times 4x &= 3 + 4 \times x + x \\ &= 7 \times 2x \\ &= 14x \end{align*}\]

What went wrong? Write the correct solution.

Mixed practice

Complete these (remember: add or multiply?):

  1. \(5x + 3x\)

  2. \(4 \times 3y\)

  3. \(2a \times 6a\)

  1. \(8m - 3m\)

  2. \(7 \times 2p\)

  3. \(4x \times 5x\)

Your turn

If \(3x \times \square x = 15x^2\), what number goes in the box?

Simplify: \(2a \times 3a + 4a^2\)

Is \(5m \times 2m\) the same as \(2m \times 5m\)? Explain why.

Summary

Today we learned:

  • When multiplying term × term:
    • multiply everything together (including the pronumerals)

Key difference compared to gathering like terms :

  • \(3x + 2y\) (can’t do anything as not like terms)
  • \(3x \times 2y = 6x^2\) (doesn’t matter if like terms or not)

Exit task

On scrap paper, write your name, then complete:

  1. \(6 \times 4a = ?\)
  2. \(3m \times 5m = ?\)
  3. What’s the difference between \(2x + 3x\) and \(2x \times 3x\)?