Nalanda College, Colombo 10 Grade 11 Maths Worksheet: 6 Binomial Expressions

Expand the square of a binomial with a minus sign

Answer: 16x² − 24x + 9

💡 What it's asking: We must open up a bracket that is squared. A 'binomial' is a bracket with two terms, and there is a ready-made pattern for squaring one with a minus sign.

1. 1Remember the pattern: (a − b)² = a² − 2ab + b².
2. 2Match the bracket to the pattern: a = 4x and b = 3.
3. 3First term: (4x)² = 16x² (square both the 4 and the x).
4. 4Middle term: 2 × 4x × 3 = 24x, and it takes the minus sign: −24x.
5. 5Last term: 3² = 9, so the answer is 16x² − 24x + 9.

✅ Put x = 1: (4 − 3)² = 1, and 16 − 24 + 9 = 1, so it matches.

Square a number near 100 using a binomial

Answer: 9801

💡 What it's asking: Squaring 99 by long multiplication is slow. If we write 99 as 100 − 1, the binomial pattern makes it quick mental maths.

1. 1Write 99 as 100 − 1, because 100 is easy to work with.
2. 2Use (a − b)² = a² − 2ab + b² with a = 100, b = 1.
3. 3a² = 10000, 2ab = 2 × 100 × 1 = 200, b² = 1.
4. 4So 99² = 10000 − 200 + 1 = 9801.

✅ 99² must be a little less than 100² = 10000, and 9801 is, so it makes sense.

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