Square of a Binomial
Apply the square of a binomial formula in Grade 9 algebra: (a+b)²=a²+2ab+b² and (a-b)²=a²-2ab+b², avoiding the common mistake of forgetting the middle term.
Key Concepts
Property $(a + b)^2 = a^2 + 2ab + b^2$ $(a b)^2 = a^2 2ab + b^2$.
Explanation Squaring a binomial means multiplying it by itself, not just squaring the two terms inside! This special pattern is a shortcut so you don't have to use FOIL every time. Just square the first term, square the last term, and find twice their product for the middle. It’s a handy trick for perfect square trinomials.
Examples $(x + 5)^2 = x^2 + 2(x)(5) + 5^2 = x^2 + 10x + 25$ $(2x 4)^2 = (2x)^2 2(2x)(4) + 4^2 = 4x^2 16x + 16$ $(3t 1)^2 = (3t)^2 2(3t)(1) + 1^2 = 9t^2 6t + 1$.
Common Questions
What is the formula for the square of a binomial?
The square of a binomial follows the pattern (a + b)² = a² + 2ab + b². The three terms are: the square of the first term, twice the product of both terms, and the square of the second term.
What is the most common mistake when squaring a binomial?
The most frequent error is writing (a + b)² = a² + b², forgetting the middle term 2ab. For example, (x + 3)² is NOT x² + 9 — it is x² + 6x + 9, where 6x is the critical middle term.
How do you expand (2x - 5)² using the binomial square formula?
Identify a = 2x and b = 5. Apply (a - b)² = a² - 2ab + b²: (2x)² - 2(2x)(5) + 5² = 4x² - 20x + 25. Always remember all three terms.