VC2M9A02 Official strand: Algebra

Expand and factorise expressions

Practise online with Next and Previous buttons, worked explanations and a report of the questions to review.

Use the distributive law, collect like terms and reverse an expansion to factorise monic quadratics.

One-question preview

Choose one answer

Try this sample, or continue to the online quiz for a practice set with Next and Previous buttons.

Expand (x + 1)(x + 2).

Ax² + 4x + 2 Bx² + 3x + 2 Cx² + 3x + 3 Dx² + 2x + 3

This preview contains one question. Continue to a practice set for more questions.

Show worked steps

Answer: x² + 3x + 2

Multiply x and 1 by both terms in the second bracket.
The middle terms are 2x and 1x.
Collect them to get x² + 3x + 2.

This is a question from this topic’s quiz. Preview answers are not saved.

Scratchpad

Working out

Your thinking space

Draw with a finger, pen or mouse, or type your working below.

Typed working

Your working stays on this page. It is not submitted or saved, and clears when you leave or reload.

Curriculum reference

Victorian Curriculum F–10 Version 2.0

Pi Leo practice scope

Use the distributive law, collect like terms and reverse an expansion to factorise monic quadratics.

Read the official VCAA curriculum description (VC2M9A02)

These quizzes practise concepts within this topic. Multiple-choice answers alone do not demonstrate drawing, conducting an investigation or using a digital tool.

Activities to practise beyond the quiz

Supported by the guided activity; selecting an MCQ does not demonstrate this action.

VC2M9A02-C01Multiply each term in one binomial by each term in the other.
VC2M9A02-C02Find integer factors with the required product and sum.
VC2M9A02-C03Create and communicate an area or algebraic explanation.
VC2M9A02-C04Apply and explain expand and factorise expressions using calculate and explain each step.
VC2M9A02-C05Apply and explain expand and factorise expressions using work backwards from what is known.

Learn with worked examples

Help with this topic

Open complete study note

Skills in this topic

Traceable coverage

Subskills

These practice subskills map to the curriculum topic. Guided activities cover skills beyond multiple-choice questions.

Descriptor-derived subskills

D01
Expand two bracketsMultiply each term in one binomial by each term in the other.
D02
Reverse an expansionFind integer factors with the required product and sum.
D03
Calculate and explain each stepApply and explain expand and factorise expressions using calculate and explain each step.
D04
Work backwards from what is knownApply and explain expand and factorise expressions using work backwards from what is known.