CLASS 8 MATHS · ALGEBRAIC EXPRESSIONS AND IDENTITIES

Expand using algebraic identities

(a + b)(a − b) = a² − b², (a ± b)² = a² ± 2ab + b², (x + a)(x + b) = x² + (a + b)x + ab.

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Worked examples

Example 1 · level 1

Expand (x + 9)(x − 9).

x² − 18x − 81
x² − 9
x² − 81
x² + 81

Show solution

a = x, b = 9.
a² = x², b² = 81.
Answer: x² − 81.

Answer: x² − 81

Example 2 · level 2

Expand (x + 3)(x + 1).

x² + 4x + 3
x² + 4x − 3
x² + 3
x² + 3x + 4

Show solution

a + b = 3 + 1 = 4.
ab = 3 × 1 = 3.
So (x + 3)(x + 1) = x² + 4x + 3.

Answer: x² + 4x + 3

Example 3 · level 3

Use an identity to find 56².

Show solution

56² = (50 + 6)².
Using (a + b)² = a² + 2ab + b²: 2,500 + 600 + 36.
= 3,136.

Answer: 3,136