Distributive Law

The distributive law says that to multiply a bracket you multiply every part inside it, then add or subtract the results. In NSW Year 7 maths (NESA outcome MA4‑ALG‑C‑01) it is used first with numbers and then with pronumerals, so \(2(x + 5)\) becomes \(2x + 10\).

You will split awkward numbers into friendly sums or differences, for example \(18 \times 12 = 18 \times (10 + 2) = 216\) or \(72 \times (100 - 1)\), and link the law to a rectangle’s area when it is cut into two parts. Then you start expanding brackets. It is handy for pricing 12 items at $49 each without a calculator. This subtopic is part of Year 7 Algebra and Equations.