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Expanding and factorising

Expand expressions with brackets using the distributive law, and factorise simple expressions by taking out the highest common factor.

Worked examples

Expanding a single bracket

Straightforward

Problem

Expand 5(x+3)5(x + 3).

Expanding two brackets and simplifying

Moderate

Problem

Expand and simplify 3(x+4)+2(x−1)3(x + 4) + 2(x - 1).

Factorising by taking out a common factor

Challenging

Problem

Factorise 12x+812x + 8.

Practise

Q1·Straightforward
Expand 3(x+4)3(x + 4). What is the constant term in the result?
Q2·Straightforward
Expand 2(m+5)2(m + 5). What is the coefficient of mm in the result?
Q3·Straightforward
Expand 4(y−3)4(y - 3). What is the constant term in the result?
Q4·Straightforward
Expand 5(2a+1)5(2a + 1). What is the coefficient of aa in the result?
Q5·Moderate
Expand and simplify 2(x+3)+3(x+1)2(x + 3) + 3(x + 1). What is the coefficient of xx in the result?
Q6·Moderate
Expand and simplify 4(m+2)−2(m+3)4(m + 2) - 2(m + 3). What is the coefficient of mm in the result?
Q7·Moderate
Expand and simplify 3(2y+1)+2(y−4)3(2y + 1) + 2(y - 4). What is the coefficient of yy in the result?
Q8·Moderate
Expand and simplify 5(a−1)−2(2a−3)5(a - 1) - 2(2a - 3). What is the coefficient of aa in the result?
Q9·Challenging
Factorise 6x+96x + 9. What is the highest common factor (HCF) of the two terms?
Q10·Challenging
Which is the fully factorised form of 10m−1510m - 15?
Q11·Challenging
Factorise 8y+128y + 12. What is the highest common factor (HCF) of the two terms?
Q12·Challenging
Which is the fully factorised form of 14a−21b14a - 21b?