Algebraic Identities

Master (a+b)² and more visually.

Core Concepts

Algebraic identities are shortcuts. Instead of multiplying everything out, we use patterns.

(a + b)² = a² + 2ab + b²
Think of it as a big square made of two smaller squares (a² and b²) and two rectangles (ab).

(a + b)(a - b) = a² - b²
The middle terms cancel out!
Useful for 52 × 48 = (50+2)(50-2) = 2500 - 4 = 2496.

Question: Expand.

• a = x, b = 3.

• a² + 2ab + b²

• x² + 2(x)(3) + 3²

• Answer: x² + 6x + 9.

Question: Expand.

• a = 2x, b = 5.

• a² - 2ab + b²

• (2x)² - 2(2x)(5) + 5²

• Answer: 4x² - 20x + 25.

Question: Calculate mentally.

• (100 + 3)²

• 100² + 2(100)(3) + 3²

• 10000 + 600 + 9

• Answer: 10609.

Question: Calculate.

• Use a² - b² = (a+b)(a-b).

• (65+35)(65-35)

• 100 × 30

• Answer: 3000.