Factorization is the reverse operation of expansion. It changes an expression into a product, and the basic first step is to find and factor out common factors.
Factoring Out Common Factors
Find the factors common to each term and take them outside the parentheses.
ab + ac = a(b + c)
- 3x² + 6x = 3x(x + 2)
- 4a²b − 8ab² = 4ab(a − 2b)
- x(a + b) + y(a + b) = (a + b)(x + y)
Example ①
(1) 6x² − 9x (2) 12a²b + 8ab²
Answer:(1) 3x(2x − 3) (2) 4ab(3a + 2b)
(1) 6x² − 9x (2) 12a²b + 8ab²
Answer:(1) 3x(2x − 3) (2) 4ab(3a + 2b)
Expressions as Common Factors
You can also factor out a common part when it is an expression in parentheses.
Example ②
Factor (x − 1)a + (x − 1)b.
Answer:Factoring out the common factor (x − 1) gives (x − 1)(a + b)
Factor (x − 1)a + (x − 1)b.
Answer:Factoring out the common factor (x − 1) gives (x − 1)(a + b)
Key Points
- Take out the greatest common factor of the numbers and variables in each term
- After factoring out, organize the expression inside the parentheses neatly
- An expression can also be factored out as a common part
Practice Problems
- Factor 15a² − 10a.
- Factor 2x²y − 6xy² + 4xy.
- Factor a(x + y) − b(x + y).
Answers and Explanations
- Answer:5a(3a − 2)
Explanation: Factor out the common factor 5a. - Answer:2xy(x − 3y + 2)
Explanation: The common factor is 2xy. - Answer:(x + y)(a − b)
Explanation: Factor out (x+y).