Solve for x in (x+1)(2x+1) = 2x²+4: Expanding Binomial Products

Let's solve the equation, first we'll simplify the algebraic expressions using the extended distribution law:

$(a+b)(c+d)=ac+ad+bc+bd$We will therefore apply the mentioned law and open the parentheses in the expression in the equation:

$(x+1)(2x+1)=2x^2+4 \\ 2x^2+x+2x+1=2x^2+4 \\$We'll continue and combine like terms, by moving terms, then - we can notice that the term with the squared power cancels out and therefore it's a first-degree equation, which we'll solve by isolating the variable term on one side and dividing both sides of the equation by its coefficient:

$2x^2+x+2x+1=2x^2+4\\ 3x=3\hspace{8pt}\text{/}:3\\ \boxed{x=1}$Therefore, the correct answer is answer B.