If a - b = 8 and 4ab = 84, then what is the value of $3a^2 - 3b^2$ ?
Answer & explanation
Correct answer: option 4
We know = a³ - b³ = (a - b)(a² + ab + b²)
a - b = 8
4ab = 84
ab = 21
= 3a³ - 3b³ = 3(a³ - b³)
= 3(a - b)(a² + ab + b²)
= (a - b)2 = a2 + b2 - 2ab
= 82 = a2 + b2 - 2 × 21
= 64 = a2 + b2 - 42
= a2 + b2 = 106
Put the all values in3(a - b)(a² + ab + b²)
= 3 × 8 × (106 + 21) = 3048