James and Reshma were talking about algebraic identities they learnt in school. James Class 9

James and Reshma were talking about algebraic identities they learnt in school. James Class 9

Question 1.

James and Reshma were talking about algebraic identities they learnt in school. James: (a - b)² (a + b) = (a² - 2ab + b²)(a + b) Reshma: I have a different idea. Class 9

(a-b)² (a + b) = (a - b) [(a - b) (a + b)] = (a - b) (a² - b²)

I will find this product to get the answer. According to you, who is correct and why? Try to combine more such identities and find new results.

Answer:

James first uses the identity:

(a - b)² = a² - 2ab + b²

He first expressed (a - b)² in expanded form and then multiplied the result by (a + b).

Reshma first uses the identity:

(a + b) (a-b) = a² - b²

She first grouped one factor (a - b) with (a + b), and then applied the identity to simplify the expression.

Both James and Reshma are correct. They used different identities to simplify the same expression, and both methods gave the same final result. Some new algebraic results obtained by combining identities are:

(a + b)² - (a - b)² = 4ab

(a² + b²) (a² - b²) = a⁴ - b⁴

[Note: Many other identities can also be formed in a similar manner.]