Square of a difference
Apply the square of a difference pattern (a-b)²=a²-2ab+b² in Grade 10 algebra to expand binomials quickly and recognize perfect square trinomials in factoring problems.
Key Concepts
The square of a binomial difference follows the pattern: $(a b)^2 = (a b)(a b) = a^2 2ab + b^2$.
Example 1: $(3y 7)^2 = (3y)^2 2(3y)(7) + 7^2 = 9y^2 42y + 49$. Example 2: $(k 6)^2 = k^2 2(k)(6) + 6^2 = k^2 12k + 36$.
Just like squaring a sum, squaring a difference has a special pattern to save you time. When you multiply $(a b)$ by itself, the 'Outside' and 'Inside' terms are both negative, combining to create the middle term $ 2ab$. Remembering this formula helps you avoid common errors and solve these problems in a single, confident step without writing out FOIL.
Common Questions
What is the formula for the square of a difference?
(a-b)² = a²-2ab+b². For example, (x-3)² = x²-6x+9.
How do you apply (a-b)² to expand (2x-5)²?
With a=2x and b=5: (2x)²-2(2x)(5)+5² = 4x²-20x+25.
How does recognizing perfect square trinomials help with factoring?
If a trinomial matches a²-2ab+b², it factors as (a-b)². For example, x²-10x+25 = (x-5)² because 25=5² and 10x=2·x·5.