Question

If ab = 8 and a^2+b^2=16, then what is the value of (a+b)^2?

Answer 1

First, we can start by expanding (a+b)²

a²+2ab+b²

We can then use the commutative property to separate this into:

a²+b² + 2ab

Since we are given the values for a²+b² and ab, we can plug in these values into the equation:

16 + (2)(8)
16+16
32

Therefore, the value of (a+b)² is 32

Answer 2

(a + b)^2 = a^2 + 2ab + b^2
Given
ab = 8
a^2 + b^s = 16

Substitute and solve
a^2 + 2ab + b^2
a^2 + b^2 = 16
ab = 8
2ab = 16

Therefore a^2 + 2ab + b^2 = 32 <<<< answer