Simplify the following.
(2x +3)² − (x + 1)².

Correct option is A

Given:

​$$(2x + 3)^2 - (x + 1)^2$$​​

Formula Used:

Difference of squares: $$A^2 - B^2 = (A-B)(A+B)$$​​

Binomial square:$$(a+b)^2 = a^2 + 2ab + b^2$$​​

Solution:
Using difference of squares with A = 2x + 3, B = x + 1:
​$$(2x+3)^2 - (x+1)^2 = \big[(2x+3)-(x+1)\big]\big[(2x+3)+(x+1)\big]$$​​
= (x + 2)(3x + 4)
= $$3x^2$$​+ 10x + 8.