Maths worksheets · lesson 61 of 64 · free

Algebraic identities — Maths worksheet

Identities are true for every value of the letters: (a + b)² = a² + 2ab + b², (a − b)² = a² − 2ab + b² and (a + b)(a − b) = a² − b². They make mental maths easy: 103² = (100 + 3)² = 10000 + 600 + 9 = 10609, and 53 × 47 = (50 + 3)(50 − 3) = 2500 − 9 = 2491.

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The method

Split into easy parts — “write a hard number as a round number plus or minus a small one”

  1. (a + b)² = a² + 2ab + b².
  2. (a − b)² = a² − 2ab + b².
  3. (a + b)(a − b) = a² − b²; so a² − b² = (a + b)(a − b).
  4. a² + b² = (a + b)² − 2ab = (a − b)² + 2ab.

Use it for: Quick multiplication in your head, checking long multiplication, and the algebraic expressions and identities chapter of Class 8 maths.

Worked example: Use (a + b)(a − b) = a² − b² to find 53 × 47. → 2491

  1. 53 × 47 = (50 + 3)(50 − 3) = 50² − 3².
  2. 2500 − 9 = 2491.

Check: 53 × 47 = 53 × 40 + 53 × 7 = 2120 + 371 = 2491 ✓

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🏁 Lesson 61 test

20 sums. Check each answer, then go to the next one. Get 16 or more right to pass.

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🖨️ Class 8 Maths Worksheet: Algebraic Identities

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