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Algebra · JSS 2, JSS 3

Perfect squares

Expand a bracket squared in one step.

  • (a + b)2 = a2 + 2ab + b2
  • (a − b)2 = a2 − 2ab + b2

What the letters mean

a, b
any numbers or terms

Worked example

Use (a + b)2 to work out 1022 without a calculator.

  1. Step 1: Write 102 as 100 + 2

    1022 = (100 + 2)2

  2. Step 2: Expand

    = 1002 + 2 × 100 × 2 + 22

    = 10,000 + 400 + 4

  3. Step 3: Add

    = 10,404

Final answer: 10,404

(a + b)2 is not a2 + b2: don't forget the middle term 2ab.

See it

Play with this picture from the Expanding Brackets lesson.

x344x12

Each part's area = its side × its top. Dashed pink parts are negative.

Sides: 4(x + 3)

Parts: 4x + 12

Area = 4x + 12

Outside number4
x-number inside1
Number inside3