With factoring, you rewrite an addition as a product. You bring back the parentheses to make an expression more organized. This is an indispensable skill for solving equations and simplifying fractions.

🛠️ The Toolbox

Use these six basic techniques to factor algebraic terms:

#	Method / Property
1.	ab + ac = a(b + c) (Common factor)
2.	ac + ad + bc + bd = (a + b)(c + d)
3.	a² + 2ab + b² = (a + b)² (Special product)
4.	a² - 2ab + b² = (a - b)²
5.	a² - b² = (a + b)(a - b) (Difference of squares)
6.	x² + (p+q)x + pq = (x + p)(x + q) (Product-sum method)

🔍 Practical examples

See how to apply the rules above here:

Factor outside parentheses (Rule 1):

2a + 6 = 2(a + 3)

Reducing to a square (Rule 3):

x² + 14x + 49 = (x + 7)²

Difference of squares (Rule 5):

p² - 81q² = (p + 9q)(p - 9q)

Product-sum method (Rule 6):

x² + 8x + 15 = (x + 3)(x + 5)

💡

Check yourself: You can always check if you have factored correctly by expanding the parentheses again. If you get back to the original expression, your answer is correct!