Expand double brackets, then run it backwards: factorise x² + bx + c, a difference of two squares and common factors.
What you will learn
- Expand (x + a)(x + b) and (x + a)²
- Factorise x² + bx + c
- Spot a difference of two squares
Every term times every term
A quadratic expression has x² as its highest power, such as x² + 8x + 15.
To expand two brackets, multiply each term in the first by each term in the second, then collect like terms.
- (x + 3)(x + 5)
- x × x = x², x × 5 = 5x, 3 × x = 3x, 3 × 5 = 15
- x² + 5x + 3x + 15
- = x² + 8x + 15
Squared brackets are two brackets: (x + 4)² = (x + 4)(x + 4) = x² + 8x + 16. It is not x² + 16. That missing middle term is the most common lost mark in this topic.
Numbers in front of x multiply too: (2x + 3)(4x − 1) = 8x² − 2x + 12x − 3 = 8x² + 10x − 3.
For three brackets, expand two of them first, then multiply the answer by the third, term by term:
- (x + 1)(x + 2)(x − 3)
- (x + 1)(x + 2) = x² + 3x + 2
- (x² + 3x + 2)(x − 3) = x³ − 3x² + 3x² − 9x + 2x − 6
- = x³ − 7x − 6
The rest of this lesson and its 6 practice questions are locked.
In this lesson
- Every term times every term
- Factorising runs it backwards
- Two shortcuts
- When there is a number in front of x² (Higher)
- Try it: Same expression, same graph
6 practice questions, marked as you go; about 25 minutes in all.
Key terms
Quadratic, Multiply to c, Add to b
In this unit: Quadratics
Expand and factorise quadratics, solve them by factorising, the formula and completing the square, and read roots and turning points from graphs.
- Expanding and factorising
- Solving by factorising
- The quadratic formula
- Completing the square
- Quadratic graphs
- Algebraic fractions