Question

Factorize ( a + b)2 – ( a – b) 2​

Answer 1

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As you (should have) learned in algebra class:

(a+b)² = a² + 2ab + b² and (a-b)² = a² - 2ab + b².

Therefore (a+b)² - (a-b)² = (a² + 2ab + b²) - (a² - 2ab + b²).

Regrouping, we have (a+b)² - (a-b)² = (a²-a²) + (2ab-(-2ab)) + (b²-b²), which simplifies to 4ab.

Answer 2

Step-by-step explanation:

(a+b)² = a² + 2ab + b² and (a-b)² = a² - 2ab + b².

Therefore (a+b)² - (a-b)² = (a² + 2ab + b²) - (a² - 2ab + b²).

Regrouping, we have (a+b)² - (a-b)² = (a²-a²) + (2ab-(-2ab)) + (b²-b²), which simplifies to 4ab.