Special factorizations
This Grade 6 algebra skill from Yoshiwara Elementary Algebra covers special factorization patterns including the difference of squares, sum and difference of cubes. Students learn to recognize and factor expressions of the form a^2 - b^2 = (a+b)(a-b), a^3 + b^3, and a^3 - b^3 using standard formulas.
Key Concepts
Property 1. $a^2 + 2ab + b^2 = (a + b)^2$.
2. $a^2 2ab + b^2 = (a b)^2$.
3. $a^2 b^2 = (a + b)(a b)$.
Common Questions
What are special factorizations in algebra?
Special factorizations include patterns like the difference of squares (a^2 - b^2 = (a+b)(a-b)) and sum/difference of cubes, which can be factored using memorized formulas.
What is the difference of squares factorization?
a^2 - b^2 = (a + b)(a - b). For example, x^2 - 16 = (x + 4)(x - 4).
What is the sum of cubes formula?
a^3 + b^3 = (a + b)(a^2 - ab + b^2). For example, x^3 + 8 = (x + 2)(x^2 - 2x + 4).
How do you recognize a special factorization pattern?
Look for two perfect square terms separated by subtraction (difference of squares) or two perfect cube terms connected by addition or subtraction.
Where are special factorizations taught in Grade 6?
Special factorizations are covered in the Yoshiwara Elementary Algebra textbook for Grade 6.