Finding Special Products of Binomials
Find special products of binomials in Grade 9 algebra using three key formulas: (a+b)²=a²+2ab+b², (a-b)²=a²-2ab+b², and (a+b)(a-b)=a²-b² for fast polynomial multiplication.
Key Concepts
New Concept $$ (a + b)^2 = a^2 + 2ab + b^2 $$ $$ (a b)^2 = a^2 2ab + b^2 $$ $$ (a + b)(a b) = a^2 b^2 $$ What’s next Next, you’ll apply these patterns to multiply binomials, perform mental math tricks, and solve problems involving area.
Common Questions
What are the three special products of binomials formulas?
The three special products are: (1) (a+b)² = a² + 2ab + b² (sum squared), (2) (a-b)² = a² - 2ab + b² (difference squared), and (3) (a+b)(a-b) = a² - b² (difference of squares). Memorizing these saves significant time.
How do you use the special product formula for (3x + 2)²?
Apply (a + b)² = a² + 2ab + b² with a = 3x and b = 2: (3x)² + 2(3x)(2) + 2² = 9x² + 12x + 4. The three terms are the square of each term plus twice their product.
Why are special product formulas more efficient than FOIL?
FOIL requires four multiplications and combining terms. Special product formulas let you write the answer directly from the pattern, reducing 4 steps to 3 and virtually eliminating the most common sign errors.