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Expanding and simplifying

Expand a single bracket and collect like terms; expand the product of two binomials; expand and simplify expressions with two pairs of brackets.

Worked examples

Expanding a single bracket and collecting like terms

Straightforward

Problem

Expand and simplify 5(x+3)+2x5(x + 3) + 2x.

Expanding the product of two binomials

Moderate

Problem

Expand and simplify (x+3)(x+2)(x + 3)(x + 2).

Expanding and simplifying two pairs of brackets

Challenging

Problem

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

Practise

Q1·Straightforward
Expand and simplify 3(x+2)+4x3(x + 2) + 4x. What is the coefficient of xx?
Q2·Straightforward
Expand and simplify 2(x+5)+3x2(x + 5) + 3x.
Q3·Straightforward
Expand and simplify 4(x−3)+2x4(x - 3) + 2x. What is the constant term?
Q4·Straightforward
Expand and simplify 5(2x+1)−3x5(2x + 1) - 3x. What is the coefficient of xx?
Q5·Moderate
Expand (x+3)(x+2)(x + 3)(x + 2). What is the coefficient of xx?
Q6·Moderate
Expand (x+4)(x−1)(x + 4)(x - 1). What is the constant term?
Q7·Moderate
Expand (x−3)(x−5)(x - 3)(x - 5). What is the coefficient of xx?
Q8·Moderate
Expand (2x+1)(x+3)(2x + 1)(x + 3). What is the coefficient of xx?
Q9·Challenging
Expand and simplify (x+2)(x+3)+2(x+1)(x + 2)(x + 3) + 2(x + 1). What is the coefficient of xx?
Q10·Challenging
Expand and simplify (x+4)(x−2)+3(x−1)(x + 4)(x - 2) + 3(x - 1). What is the constant term?
Q11·Challenging
Expand and simplify (x+5)(x+1)−(x+2)(x + 5)(x + 1) - (x + 2). What is the coefficient of xx?
Q12·Challenging
Expand and simplify (2x+3)(x+4)+2(x−5)(2x + 3)(x + 4) + 2(x - 5). What is the coefficient of xx?