Square of a sum
Expand the square of a sum (a+b)²=a²+2ab+b² in Grade 10 algebra as a shortcut for multiplying binomials and recognizing perfect square trinomials in reverse for factoring.
Key Concepts
The square of a binomial sum follows the pattern: $(a + b)^2 = (a + b)(a + b) = a^2 + 2ab + b^2$.
Example 1: $(4p + 3q)^2 = (4p)^2 + 2(4p)(3q) + (3q)^2 = 16p^2 + 24pq + 9q^2$. Example 2: $(x + 5)^2 = x^2 + 2(x)(5) + 5^2 = x^2 + 10x + 25$.
Squaring a binomial isn't just squaring each piece inside! You're multiplying the binomial by itself, which requires the FOIL method. This pattern, $a^2 + 2ab + b^2$, is a fantastic time saver. It reminds you to always include the product of the 'Outside' and 'Inside' terms, which are always identical. This middle term is the secret ingredient!
Common Questions
What is the formula for the square of a sum?
(a+b)² = a²+2ab+b². For example, (x+4)² = x²+8x+16.
How do you expand (3x+2)² using the square of a sum pattern?
With a=3x and b=2: (3x)²+2(3x)(2)+2² = 9x²+12x+4.
How does recognizing (a+b)² help in factoring?
If a trinomial matches a²+2ab+b², it is a perfect square: x²+10x+25=(x+5)² because 25=5² and 10x=2(x)(5). Recognizing the pattern shortcuts the factoring process.