Using ab rather than a x b

In algebra, we often use shorthand notations to make expressions more concise and easier to manipulate. One of the most fundamental of these is writing 'ab' instead of 'a × b'. This notation is used to represent multiplication without using the multiplication symbol (×).

Key points to remember:

• When we write two letters or a number and a letter next to each other without any operation symbol, it means we're multiplying them.
• This notation applies to variables (letters) and numbers.
• The order doesn't matter for multiplication, so 'ab' is the same as 'ba'.
• This notation is particularly useful when dealing with variables and coefficients.

For example, '3x' means '3 × x', and 'abc' means 'a × b × c'.

1. Example: Write 3 × x using the shortened notation.

   Solution: 3x

   Explanation: We simply remove the multiplication sign and write the number and variable together.

2. Example: Express a × b × c using the shortened notation.

   Solution: abc

   Explanation: We remove all multiplication signs, writing the variables directly next to each other.

3. Example: Write 2 × y × 5 using the shortened notation.

   Solution: 10y

   Explanation: First, we multiply the numbers: 2 × 5 = 10. Then we write this next to y: 10y.

4. Example: Express (x + 2) × y using the shortened notation.

   Solution: (x + 2)y

   Explanation: We keep the brackets to maintain the order of operations and simply remove the multiplication sign.

5. Example: Write 2.5 × a × b using the shortened notation.

   Solution: 2.5ab

   Explanation: We keep the decimal number as it is and write it directly next to the variables.

1. Write 4 × z using the shortened notation.

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2. Express x × y using the shortened notation.

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3. Write 7 × a × b using the shortened notation.

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4. Express 3 × x × 2 using the shortened notation.

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5. Write m × n × p using the shortened notation.

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6. Express (y + 1) × x using the shortened notation.

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7. Write 0.5 × c × d using the shortened notation.

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8. Express (2x + 3) × (y - 1) using the shortened notation.

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9. Write 2a × 3b × 4c using the shortened notation.

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10. Express (x² + 2x + 1) × y × (z - 2) using the shortened notation.

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