Brackets should be expanded in the following ways:
For an expression of the form a(b + c), the expanded version is ab + ac, i.e., multiply the term outside the bracket by everything inside the bracket (e.g. 2x(x + 3) = 2x² + 6x [remember x × x is x²])
For an expression of the form (a + b)(c + d), the expanded version is ac + ad + bc + bd, in other words everything in the first bracket should be multiplied by everything in the second.
Expand (2x + 3)(x - 1):
(2x + 3)(x - 1)
= 2x² - 2x + 3x - 3
=2x² + x - 3
Factorising is the reverse of expanding brackets, so it is putting 2x² + x - 3 into the form (2x + 3)(x - 1). This is an important way of solving quadratic equations.
The first step of factorising an expression is to 'take out' any common factors which the…