Example Card: Product of a Sum and Difference
Apply the difference of squares pattern in Grade 9 algebra: multiply (a+b)(a-b) to get a²-b² instantly, eliminating the middle term for fast polynomial multiplication.
Key Concepts
Watch how multiplying a sum and a difference makes the middle term vanish!
Example Problem.
Find the product: $(4x + 7)(4x 7)$.
Common Questions
What is the product of a sum and difference pattern?
When multiplying (a + b)(a - b), the middle terms cancel out and you get a² - b². For example, (4x + 7)(4x - 7) simplifies directly to 16x² - 49.
Why does the middle term disappear when multiplying a sum and difference?
The outer and inner products are +ab and -ab, which add to zero. This special structure means only the difference of the squares of the two terms remains.
How do you recognize when to use the difference of squares shortcut?
Look for two sets of parentheses with identical terms but opposite signs — one with addition and one with subtraction. When you see (x + n)(x - n), the answer is always x² - n².