Expanding brackets

To ‘expand’ an expression means to remove the brackets. Any terms outside of the bracket need to be multiplied by what is inside the brackets.

Expanding single brackets
Expand $$a(4b+8)$$


 * Step one: Multiply the term outside the bracket by the first term inside the bracket:

$$a \times 4b = 4ab$$


 * Step two: Multiply the term outside the bracket by the second term inside the bracket:

$$a \times 8 = 8a$$


 * Step three: Put the two terms together:

$$4ab + 8a$$

If there is more than one term outside the bracket the same rule applies - everything outside the bracket must be multiplied by what's inside.

Expand $$4a (3a + 5)$$

Step one: 4a x 3a = 12a²

Step two: 4a x 5 = 20a

Step three: 4a ( 3a + 5 ) = 12a² + 20a 

Expanding double brackets
Expand and simplify $$(x+8)(x-5)$$

To answer this question you will need to remember the acronym FOIL, which stands for First, Outer, Inner, Last.


 * Step one: Multiply the first terms in each bracket together:

$$x \times x = x^2$$


 * Step two: Multiply the outer terms (the first term in the first bracket and the second term in the second bracket) together:

$$x \times -5 = -5x$$


 * Step three: Multiply the inner terms (the second term in the first bracket and the first term in the second bracket) together:

$$8 \times x = 8x$$


 * Step four: Multiply the last terms (the second term in each bracket) together:

$$8 \times -5 = -40$$


 * Step five: Combine the four terms to form an expression:

$$x^2 - 5x + 8x - 40$$


 * Step six: Simplify the expression to find your answer:

$$x^2 + 3x - 40$$

Expanding squared brackets
Expand and simplify $$(x+3)^2$$


 * Step one: Write out the expression as double brackets. Squaring an expression is multiplying the expression by itself.

$$(x+3)(x+3)$$


 * Step two: Expand the brackets using the FOIL method described above:

$$x^2 + 3x + 3x + 9$$


 * Step three: Simplify by collecting like terms:

$$x^2 + 6x + 9$$

Exam practice questions

 * 1.
 * (a) Expand $$3(x+5)$$
 * (b) Expand and simplify $$4(y+10) - 2(4-2y)$$
 * 2.
 * (a) Expand and simplify $$(z+2)(z-7)$$
 * (b) Expand and simplify $$(x-2)^2$$

Answers
Click 'Expand' on the bottom right of this section to see the answers.


 * 1.
 * (a) 3x+15
 * (b) 8y+32
 * 2.
 * (a) z2-5z-14
 * (b) x2-4x+4