Explain the following in your own words: (a + b)2 ≠ a2 + b2. Give a numerical example to illustrate this.

I assume you mean (a + b)² ≠ a² + b²
since (a + b)² = a² + 2ab + b²
they are clearly not equal unless a or b or both are 0.
pick any nonzero values for a and b and do the math.
a = 3, b = 5
(a + b)² = (3 + 5)² = 8² = 64 but
a² + b² = 3² + 5² = 9 + 25 = 34

Well clearly it's saying that they don't equal to each other... BUT THEY DO For example:
Let's say A = 1 and B = 3

(1+3)2 ≠ 1(2) + 3(2)
(4)2 ≠ 2 + 6
8 ≠ 8

No matter what numbers you plug in for A or B, you will always find the both sides equal. I'd say this question is "NO SOLUTION" or there's some type of error or typo.

CAUTION: I may be doing this wrong, if the a2 and b2 are exponents, I'm doing it incorrect. The person above me maybe right. I need a better view of this equation.

2a + 2b Can't equal a² + b².

For example, let:
a = 1
b = 2

2(1) + 2(2) ≠ (1)² + (2)²

2 + 4 ≠ 1 + 4

6 ≠ 5