Prime factor decomposition is to turn an integer into a product of prime numbers and remove the composite number from the factor;

Factorization is to turn algebraic expressions into products of factors and minimize the number of factors.

Specific methods,

The first step is to extract the common factor.

This is also the simplest method.

Common factors include not only coefficients, letters and monomials (I believe everyone is familiar with them),

In addition, the common factor can also be a formula,

For example, (a+b)(3m+2n)+(2m+3n)(a+b), the common factor is (a+b).

Original formula = (a+b )( 3m+2n+2m+3n)

=(a+b)(5m+5n)- So the coefficient 5 is extracted again.

= 5( a + b )( m + n)

The second step is the formula method.

Is to reverse the formula of algebraic expression multiplication,

A "-b "=(a-b)(a+b)- square difference,

A "+2ab+b "=(a+b)"- complete sum of squares,

A "-2ab+b "=(a-b)"- complete square difference,

A "'+b"' =(a+b)(a "-a b+ b ")- cubic sum,

A "'-b"' =(a-b)(a "+a b+ b ")- cubic difference,

Familiarity with formulas, squares and cubes is the key.