lesson
Distribution works on every term
1 · Learn
Expanding brackets distributes multiplication across each term: 3(x + 4) = 3x + 12. Factorising reverses that process by identifying a common factor. A negative multiplier changes both terms according to signed multiplication.
Check a proposed identity using structure, not only a single convenient value. Substitution can detect an error but one matching result is not a full proof.
2 · Worked example
2(3x - 5) = 6x - 10. Conversely, 8x + 12 = 4(2x + 3) because 4 divides both terms.
3 · Your turn
Expand -3(x - 2) and factorise 6y + 15 using the greatest common whole-number factor.
Check your answer
-3x + 6; 3(2y + 5).
4 · Apply your learning
Draw an area model for a positive example and use signed arithmetic to explain the negative example.
Adult guidance and safety
Require a reasoned method and an independent check. Use accurate number lines, geometric drawings and data displays where the task needs them. These text models require varied practice and diagnostic assessment before curriculum approval.
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Check a calculation · Year 5 onward
Use this only when your teacher or adult allows a calculator for the task. Show your thinking first. It does not replace mental or written arithmetic and does not mark your lesson answer.
Powers, roots and trigonometry · Year 7 onward
Use only when the task allows a calculator. Choose one operation at a time and record your working. Trigonometry here always uses degrees (DEG), not radians. Inverse sine, cosine and tangent return an angle, not a reciprocal. Keep exact fractions and π in answers when requested.
Approximate numerical results use up to 12 significant digits. Inverse sine returns −90° to 90°, inverse cosine 0° to 180°, and inverse tangent −90° to 90°; these are principal values, not every possible solution of a trigonometric equation.
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