Home

Maths

Algebra

Double and triple brackets - Higher

Select Lesson

Exam Board

Select an option

Statistics

Sets and Venn diagrams

Sampling and bias

Collecting data: types and classes of data

Mean, median, mode and range

Simple charts and graphs

Pie charts

Scatter graphs

Frequency tables: finding averages

Grouped frequency tables

Box plots - Higher

Cumulative frequency - Higher

Histograms and frequency density - Higher

Interpreting data

Comparing data sets

Probability

Basics of probability

Calculating theoretical probabilities

Probability: Expected and relative frequency

The AND / OR rules

Probability tree diagrams

Conditional probability - Higher

Experimental probability: frequency trees

Trigonometry

Pythagoras' theorem

Sin, cos, tan

Trigonometry: Finding angles and sides

Exact trigonometric values

Sine and cosine rules - Higher

3D Pythagoras - Higher

3D Trigonometry - Higher

Vectors

Vectors - Higher

Angles and geometry

Angles: types, notation and measuring

Basic angle rules

Angles in parallel lines

Circle theorems - Higher

Constructing triangles: SSS, SAS, ASA

Construction: angle and perpendicular bisectors

Construction: Loci

Bearings

Maps and scale drawings

Shapes and area

Properties of 2D shapes

Congruence: conditions for congruent triangles

Similar shapes: Scaling

The four transformations

Area and perimeter: Formulae

Area and circumference of circles: Formulae

3D shapes: faces, edges, vertices

Surface area of 3D shapes: Nets, formulae

Volume of 3D shapes: Formulae

Volume of 3D shapes: Comparing, rates of flow

Area and volume scale factors

Projections and elevations of 3D shapes

Ratio proportion and rates of change

Ratio

Direct and inverse proportion

Finding percentages and percentage change

Compound growth and decay

Converting units: metric and imperial

Converting units: area and volume

Time intervals: converting units of time

Speed, density and pressure: Formulae and units

Graphs

Coordinates and midpoints

Straight line graphs

Drawing straight line graphs

Finding the gradient of a straight line

Equation of a straight line: y = mx + c

Coordinates and ratio

Parallel and perpendicular lines

Quadratic graphs

Reciprocal and cubic graphs

Exponential graphs and circles - Higher

Trigonometric graphs - Higher

Solving equations using graphs

Graph transformations - Higher

Real-life graphs

Distance-time graphs

Velocity-time graphs - Higher

Gradients of real-life graphs - Higher

Algebra

Number

Explainer Video

Tutor: Meera

Summary

Double and triple brackets

In a nutshell

Double brackets consist of two binomial expressions multiplied together, e.g. $(x+1)(y-3)$ , whereas triple brackets consist of three binomial expressions multiplied together, e.g. $(x-2)(x+6)(x+9)$ . The principle behind multiplying out double brackets can be extended to multiplying out triple brackets, using the FOIL method, or a multiplication grid.

Recap on multiplying double brackets

You can expand two pairs of brackets by multiplying each term in the first set of brackets by each term in he second set. This can be done by using a multiplication grid.

Example 1

Expand the brackets $(x+1)(2x-3)$

Fill in the multiplication grid

$\times$	$\boldsymbol{x}$	$\bold{+1}$
$\boldsymbol{2x}$	$2x^2$	$+2x$
$\bold{-3}$	$-3x$	$-3$

Add and simplify the results

$\begin {aligned} (x+1)(2x-3) &= 2x^2 +2x-3x-3 \\&= \underline{2x^2-x-3}\end {aligned}$

Note: when there are just two binomial expressions, you can also use the FOIL method, as discussed in the previous lesson (multiply the First terms, the Outer terms, Inside terms and the Last terms).

Expanding Triple Brackets

To expand three brackets, first expand two of the brackets, then use the result to expand with the final pair. Use a multiplication grid to help.

Example 2

Expand $(x+1)(x+2)(x+3)$

Answer

Take the first two brackets, $(x+1)(x+2)$ and multiply out using a grid.

$\times$	$\boldsymbol{x}$	$\bold{+1}$
$\boldsymbol{x}$	$x^2$	$+x$
$\bold{+2}$	$+2x$	$+2$

Add the terms and simplify

$\begin {aligned} (x+1)(x+2) &= x^2 +x+ 2x+ 2 \\ &= x^2 + 3x +2 \end {aligned}$

Substitute back into the original question

$(x+1)(x+2)(x+3) = (x^2 + 3x+2)(x+3)$

Use another multiplication grid to multiply out these two brackets

$\times$	$\boldsymbol{x^2}$	$\boldsymbol{+3x}$	$\bold{+2}$
$\boldsymbol{x}$	$x^3$	$+3x^2$	$+2x$
$\bold{+3}$	$+3x^2$	$+9x$	$+6$

Add the terms and simplify

$\begin {aligned}(x+1)(x+2)(x+3) &= (x^2+3x+2)(x+3) \\&= x^3+3x^2+2x+3x^2+9x+6 \\&= \underline{x^3 + 6x^2+11x+6} \end {aligned}$

With practice, it is possible to multiply out without using the grid, using the FOIL method to multiply the first two brackets, and then multiply each term in the result with every term in the third bracket.

Learn with Basics

Length:

Unit 1

Expanding double brackets: FOIL and multiplication grid

Unit 2

Double brackets: Expanding and factorising

Jump Ahead

Optional

Unit 3

Double and triple brackets - Higher

Final Test

Create an account to complete the exercises

FAQs - Frequently Asked Questions

What is the FOIL method when multiplying brackets?

The FOIL method can be used when multiplying out double brackets. Multiply the First terms, the Outer terms, the Inner terms and then the Last terms. Then add and simplify the result.

How do you expand triple brackets?

To expand three brackets, first expand two of the brackets, then use the result to expand with the final pair. Use a multiplication grid to help. With practice, it is possible to multiply out without using the grid, using the FOIL method to multiply the first two brackets, and then multiply each term in the result with every term in the third bracket.

What are double or triple brackets?

Double brackets consist of two binomial expressions multiplied together, e.g. (x+1)(x+2). Triple brackets consist of three binomial expressions multiplied together, e.g. (x+2)(x-1)(x+4).

Home

Maths

Algebra

Double and triple brackets - Higher

Videos

Summary

Exercises

Select Lesson

Exam Board

Select an option

Statistics

Sets and Venn diagrams

Sampling and bias

Collecting data: types and classes of data

Mean, median, mode and range

Simple charts and graphs

Pie charts

Scatter graphs

Frequency tables: finding averages

Grouped frequency tables

Box plots - Higher

Cumulative frequency - Higher

Histograms and frequency density - Higher

Interpreting data

Comparing data sets

Probability

Basics of probability

Calculating theoretical probabilities

Probability: Expected and relative frequency

The AND / OR rules

Probability tree diagrams

Conditional probability - Higher

Experimental probability: frequency trees

Trigonometry

Pythagoras' theorem

Sin, cos, tan

Trigonometry: Finding angles and sides

Exact trigonometric values

Sine and cosine rules - Higher

3D Pythagoras - Higher

3D Trigonometry - Higher

Vectors

Vectors - Higher

Angles and geometry

Angles: types, notation and measuring

Basic angle rules

Angles in parallel lines

Circle theorems - Higher

Constructing triangles: SSS, SAS, ASA

Construction: angle and perpendicular bisectors

Construction: Loci

Bearings

Maps and scale drawings

Shapes and area

Properties of 2D shapes

Congruence: conditions for congruent triangles

Similar shapes: Scaling

The four transformations

Area and perimeter: Formulae

Area and circumference of circles: Formulae

3D shapes: faces, edges, vertices

Surface area of 3D shapes: Nets, formulae

Volume of 3D shapes: Formulae

Volume of 3D shapes: Comparing, rates of flow

Area and volume scale factors

Projections and elevations of 3D shapes

Ratio proportion and rates of change

Ratio

Direct and inverse proportion

Finding percentages and percentage change

Compound growth and decay

Converting units: metric and imperial

Converting units: area and volume

Time intervals: converting units of time

Speed, density and pressure: Formulae and units

Graphs

Coordinates and midpoints

Straight line graphs

Drawing straight line graphs

Finding the gradient of a straight line

Equation of a straight line: y = mx + c

Coordinates and ratio

Parallel and perpendicular lines

Quadratic graphs

Reciprocal and cubic graphs

Exponential graphs and circles - Higher

Trigonometric graphs - Higher

Solving equations using graphs

Graph transformations - Higher

Real-life graphs

Distance-time graphs

Velocity-time graphs - Higher

Gradients of real-life graphs - Higher

Algebra

Number

Explainer Video

Tutor: Meera

Summary

Double and triple brackets

In a nutshell

Recap on multiplying double brackets

You can expand two pairs of brackets by multiplying each term in the first set of brackets by each term in he second set. This can be done by using a multiplication grid.

Example 1

Expand the brackets $(x+1)(2x-3)$

Fill in the multiplication grid

$\times$	$\boldsymbol{x}$	$\bold{+1}$
$\boldsymbol{2x}$	$2x^2$	$+2x$
$\bold{-3}$	$-3x$	$-3$

Add and simplify the results

$\begin {aligned} (x+1)(2x-3) &= 2x^2 +2x-3x-3 \\&= \underline{2x^2-x-3}\end {aligned}$

Expanding Triple Brackets

To expand three brackets, first expand two of the brackets, then use the result to expand with the final pair. Use a multiplication grid to help.

Example 2

Expand $(x+1)(x+2)(x+3)$

Answer

Take the first two brackets, $(x+1)(x+2)$ and multiply out using a grid.

$\times$	$\boldsymbol{x}$	$\bold{+1}$
$\boldsymbol{x}$	$x^2$	$+x$
$\bold{+2}$	$+2x$	$+2$

Add the terms and simplify

$\begin {aligned} (x+1)(x+2) &= x^2 +x+ 2x+ 2 \\ &= x^2 + 3x +2 \end {aligned}$

Substitute back into the original question

$(x+1)(x+2)(x+3) = (x^2 + 3x+2)(x+3)$

Use another multiplication grid to multiply out these two brackets

$\times$	$\boldsymbol{x^2}$	$\boldsymbol{+3x}$	$\bold{+2}$
$\boldsymbol{x}$	$x^3$	$+3x^2$	$+2x$
$\bold{+3}$	$+3x^2$	$+9x$	$+6$

Add the terms and simplify

$\begin {aligned}(x+1)(x+2)(x+3) &= (x^2+3x+2)(x+3) \\&= x^3+3x^2+2x+3x^2+9x+6 \\&= \underline{x^3 + 6x^2+11x+6} \end {aligned}$

Learn with Basics

Length:

Unit 1

Expanding double brackets: FOIL and multiplication grid

Unit 2

Double brackets: Expanding and factorising

Jump Ahead

Optional

Unit 3

Double and triple brackets - Higher

Final Test

Create an account to complete the exercises

FAQs - Frequently Asked Questions

What is the FOIL method when multiplying brackets?

The FOIL method can be used when multiplying out double brackets. Multiply the First terms, the Outer terms, the Inner terms and then the Last terms. Then add and simplify the result.

How do you expand triple brackets?

What are double or triple brackets?

Double brackets consist of two binomial expressions multiplied together, e.g. (x+1)(x+2). Triple brackets consist of three binomial expressions multiplied together, e.g. (x+2)(x-1)(x+4).