Term
Sum of Perfect Cubes:
a3 + b3 |
|
Definition
(a + b)(a2 - ab + b2)
This pattern appears when you have perfect cube numerical values (8, 27, 64, 125, 216, 343, 512, ...) and perfect cubes of algebraic quantities (x3, x6=(x3)2, x9=(x3)3, x12=(x3)4, ...). |
|
|
Term
Difference of Perfect Cubes:
a3 - b3 |
|
Definition
(a - b)(a2 + ab + b2)
This pattern appears when you have perfect cube numerical values (8, 27, 64, 125, 216, 343, 512, ...) and perfect cubes of algebraic quantities (x3, x6=(x3)2, x9=(x3)3, x12=(x3)4, ...). |
|
|
Term
Difference of Perfect Squares:
a2 - b2 |
|
Definition
(a - b)(a + b)
This is a convenient pattern to recognize when factoring numerators and denominators in a fraction, since you may find a common factor of a-b or a+b in both. |
|
|
Term
Sum of Perfect Squares:
a2 + b2 |
|
Definition
The sum of perfect squares does not factor into two real-valued factors, but you can complete the square by adding and subtracting a an additional term:
(a2 + b2 + 2ab) - 2ab
(a+b)2 - 2ab |
|
|
Term
Binomial sum:
a2 + 2ab + b2 |
|
Definition
(a + b)2
This is an example of a binomial expansion of form (a + b)n with n=2. It's worth memorizing this product! |
|
|
Term
Binomial difference:
a2 - 2ab + b2 |
|
Definition
(a - b)2
This is an example of a binomial expansion of form (a - b)n with n=2. It's worth memorizing this product! |
|
|
Term
Quadratic Formula:
ax2 + bx + c = 0 |
|
Definition
This yields two solutions, which are real-valued if b2≥4ac:
|
|
|
