Multiply (2x-3)(6x+2) find and explain the error in the student’s work above

Answer 1

The correct way to multiply (2x - 3)(6x + 2) is to use the distributive property.

(2x - 3)(6x + 2) = 2x * 6x + 2x * 2 - 3 * 6x - 3 * 2
= 12x^2 + 4x - 18x - 6
= 12x^2 - 14x - 6

The error in the student's work is that they are missing the terms -18x and -6 in their result. It appears that they only multiplied the first terms (2x * 6x = 12x^2) and the last terms (-3 * 2 = -6), but they failed to multiply the outer terms (2x * 2 = 4x) and the inner terms (-3 * 6x = -18x) as well.