Sec 2 Maths · Expansion and factorisation of quadratic expressions

Expanding questions with answers

Practice questions on expanding, from the basics up to exam level, each with a full worked solution. Try them on paper first, then open the solution to check your working.

Worked example

Expand $(x + 2)^2$ .

x

+2

x

+2

Step 1 of 5

Set up the box

Write one bracket down the side (

x

and

+2

) and the other across the top (

x

and

+2

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Questions

Question 1(x + a)(x + b), all positive
Expand and simplify $(x + 7)(x + 9)$ .
Show the worked solution
$x$
$+9$
$x$
$+7$
Step 1 of 5
Set up the box
Write one bracket down the side ( $x$ and $+7$ ) and the other across the top ( $x$ and $+9$ ).
Question 2(x ± a)(x ± b) with negatives
Expand and simplify $(x - 1)(x + 2)$ .
Show the worked solution
$x$
$+2$
$x$
$-1$
Step 1 of 5
Set up the box
Write one bracket down the side ( $x$ and $-1$ ) and the other across the top ( $x$ and $+2$ ).
Question 3(ax + b)(cx + d)
Expand and simplify $(4x + 6)(x - 6)$ .
Show the worked solution
$x$
$-6$
$4x$
$+6$
Step 1 of 5
Set up the box
Write one bracket down the side ( $4x$ and $+6$ ) and the other across the top ( $x$ and $-6$ ).
Question 4Perfect squares
Expand $(3x + 3)^2$ .
Show the worked solution
$3x$
$+3$
$3x$
$+3$
Step 1 of 5
Set up the box
Write one bracket down the side ( $3x$ and $+3$ ) and the other across the top ( $3x$ and $+3$ ).
Question 5Difference of two squares
Expand and simplify $(3x + 8)(3x - 8)$ .
Show the worked solution
$3x$
$-8$
$3x$
$+8$
Step 1 of 5
Set up the box
Write one bracket down the side ( $3x$ and $+8$ ) and the other across the top ( $3x$ and $-8$ ).

More on expansion and factorisation of quadratic expressions

Notes: Expansion and factorisation of quadratic expressions Worksheet with answers (PDF)

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Questions

Question 1(x + a)(x + b), all positive

Expand and simplify $(x + 7)(x + 9)$ .

Show the worked solution

x

+9

x

+7

Step 1 of 5

Set up the box

Write one bracket down the side (

x

and

+7

) and the other across the top (

x

and

+9

Question 2(x ± a)(x ± b) with negatives

Expand and simplify $(x - 1)(x + 2)$ .

Show the worked solution

x

+2

x

-1

Step 1 of 5

Set up the box

Write one bracket down the side (

x

and

-1

) and the other across the top (

x

and

+2

Question 3(ax + b)(cx + d)

Expand and simplify $(4x + 6)(x - 6)$ .

Show the worked solution

x

-6

4x

+6

Step 1 of 5

Set up the box

Write one bracket down the side (

4x

and

+6

) and the other across the top (

x

and

-6

Question 4Perfect squares

Expand $(3x + 3)^2$ .

Show the worked solution

3x

+3

3x

+3

Step 1 of 5

Set up the box

Write one bracket down the side (

3x

and

+3

) and the other across the top (

3x

and

+3

Question 5Difference of two squares

Expand and simplify $(3x + 8)(3x - 8)$ .

Show the worked solution

3x

-8

3x

+8

Step 1 of 5

Set up the box

Write one bracket down the side (

3x

and

+8

) and the other across the top (

3x

and

-8