Question

Evaluate 3(a+b)², given that a² + b² = 16 and ab = -2.

Answer 1

36

Explanation:

To evaluate 3(a+b)², we first need to expand the square of the binomial (a+b)² using the formula:

(a+b)² = a² + 2ab + b²

Substituting the given values of a², b², and ab, we get:

(a+b)² = a² + 2ab + b²

= (a² + b²) + 2ab (since a² + b² = 16)

= 16 + 2(-2)

= 12

Now, we can substitute this value in the expression 3(a+b)²:

3(a+b)² = 3(12)

= 36

Therefore, 3(a+b)² is equal to 36.