Binary operations
A binary operation combines two numbers to give one. Ordinary and are binary operations. We can also invent our own, for example . Then .
Worked exampleUsing a new operation
An operation is defined by . Find .
- Put a = 5 and b = 3.
- Calculate.
Answer:
Quadratic expressions
A quadratic expression has the form : the highest power of is 2. To expand brackets, multiply every term in one bracket by every term in the other: .
Factorisation
Try itExpand and factorise
Choose and . The expression expands to . The graph crosses the x-axis at and .
Worked exampleFactorise
Factorise .
- Find two numbers that multiply to 12 and add to 7: they are 3 and 4.
- Write the brackets.
- Check by expanding: ✓
Answer:
Key terms
- Binary operation
- A rule that combines two numbers into one.
- Expand
- Multiply out brackets.
- Factorise
- Write an expression as a product of brackets or factors.
- Quadratic
- An expression whose highest power is 2.
Summary
- A binary operation follows its own rule for two inputs.
- Expand brackets by multiplying every term by every term.
- To factorise x² + bx + c find two numbers with product c and sum b.
- a² − b² = (a − b)(a + b).