Since no examples have been given, only a generalisation can be suggested.
An expression consists of variables and constants or coefficients that are numbers.
First, look for a common factor in the numbers. For example, if all the numbers (constants and coefficients, but not exponents) are even, 2 is a common factor and can be “taken out”, that is, taken outside a parenthesis containing an expression which has been divided by the common factor.
Now look at the degree of the remaining expression. The degree is the highest power of the variable(s). If the degree is two or more, it’s possible that further factorisation can be carried out. However, not all expressions can be reduced further. The most common expressions are quadratics (degree 2) which may or may not be factorisable. For example, x²+4xy+3y² can be factorised:
(x+3y)(x+y), but x²+x+1 cannot.
Higher degree expressions may be able to be factorised. For example, 4x³+8x²+5x+3 can be factorised but it’s not obvious what the factors are. 2x+2y+xy+4 can be factorised if you spot that it can be written:
x(y+2)+2(y+2), so that y+2 is a common factor and (y+2)(x+2) is the result of factorising.
Example: 48x⁴-243 can be factorised: 3(16x⁴-81) = 3(4x²-9)(4x²+9) = 3(2x-3)(2x+3)(4x²+9).
