Expand and simplify (x+1)(2x+3).

We first expand the first set of brackets by multiplying each element of it by the second set of brackets so (x + 1)(2x + 3) = (x)(2x + 3) + (1)(2x + 3) = x(2x + 3) + (2x + 3). We can then expand out the first set of brackets brackets to get x(2x + 3) = 2x² + 3x. The second set of brackets needs no expanding as there is nothing to multiply it by so we simply remove these brackets. This gives us (x + 1)(2x + 3) = 2x² + 3x + 2x + 3. We can then simplify this by adding together the x and the 2x and the x is raised to the same power in both. This gives us (x + 1)(2x + 3) = 2x² + 5x + 3.