Question

Assertion (A): If 2a − 3b = 10, ab = −4 then 8a³ − 27b³ = 280

Reason (R): (2a − 3b)³ = 8a³ − 27b³ − 18ab (2a − 3b)

Options

• Both A and R are true, and R is the correct reason for A.

• Both A and R are true, but R is the incorrect reason for A.

• A is true, but R is false.

• A is false, but R is true.

Answer 1

Both A and R are true, and R is the correct reason for A.

Explanation:

Here, identity is correct in the reason, so let’s substitute the values.

(2a − 3b)³ = 8a³ − 27b³ − 18ab (2a − 3b)

(10)³ = 8a³ − 27b³ − 18(−4)(10)

1000 = 8a³ − 27b³ + 720

8a³ − 27b³ = 1000 − 720

8a³ − 27b³ = 280

Hence, the assertion is correct, and the reason is the correct explanation.