A^2-b^2 how does this work?

Question

(x - 2)²

how can this be (x-2)(x+2) is it because u can multiply the exponent in to get (x^2+4)? but i thought you could not do that you isntead would get

(x-2)(x-2) instead does this rule only apply for stuff like (5x+3)^2=(5x+3)(5x+3) ..(5x-3)^2=(5x-3)(5x-3) are these two correct can you explain in more deail thank you

by a² - b² = (a + b)(a - b)

Answer 1

quadratics with a positive sign  consist of 3 terms. ax^2+bx+c

they always have complex factors.. complex numbers that include "i"

u can factorise x2+9 using this, but u make it (x+3i)(x-3i)

because i^2 = -1, the sign reverses.. because it includes complex factors , the rule doesnt apply .

Answer 2

(x - 2)² is not equal to (x - 2)(x + 2)

(x - 2)^2 is (x - 2)(x - 2) or x^2 - 4x + 4

a^2 - b^2 is the difference of two squares when you factor it one factor has a plus sign one has a negative. You can't write that as one factor squared since it is not the same factor.  The other two example you gave are right since you are repeating the same factor.