Explanation:
Sure, here's a step-by-step response you can use:
"Hey, that's a good question! Let me explain why (2x + 1)^2 is not equal to 4x^2 + 1.
When we see an expression like (2x + 1)^2, we know that it means we need to multiply (2x + 1) by itself. So let's do that first:
(2x + 1)^2 = (2x + 1) x (2x + 1)
Now we can use the FOIL method to multiply these two expressions together:
(2x + 1) x (2x + 1) = 4x^2 + 2x + 2x + 1
If we simplify the middle terms by adding them together, we get:
(2x + 1) x (2x + 1) = 4x^2 + 4x + 1
So the expression (2x + 1)^2 simplifies to 4x^2 + 4x + 1, not 4x^2 + 1.
I can see why you might have thought the answer was 4x^2 + 1, since that's the first term in the expression we got. But we can't forget about the two middle terms that come from multiplying 2x and 1 together twice.
I hope that helps clear things up! Let me know if you have any more questions."