Squares of Binomials
This Grade 6 algebra skill from Yoshiwara Elementary Algebra teaches students the formulas for squaring a binomial: (a + b)^2 = a^2 + 2ab + b^2 and (a - b)^2 = a^2 - 2ab + b^2. Students learn to recognize and apply these patterns to expand binomial squares quickly without full FOIL.
Key Concepts
Property 1. $(a + b)^2 = a^2 + 2ab + b^2$.
2. $(a b)^2 = a^2 2ab + b^2$.
Examples To expand $(x + 5)^2$, we use the formula with $a=x$ and $b=5$: $(x)^2 + 2(x)(5) + (5)^2$, which simplifies to $x^2 + 10x + 25$.
Common Questions
What is the formula for the square of a binomial?
(a + b)^2 = a^2 + 2ab + b^2 and (a - b)^2 = a^2 - 2ab + b^2. These are called perfect square trinomials.
How do you square a binomial like (x + 5)?
(x + 5)^2 = x^2 + 2(x)(5) + 5^2 = x^2 + 10x + 25. Square the first term, double the product of both terms, then square the last term.
What is a common mistake when squaring a binomial?
A common error is writing (a + b)^2 = a^2 + b^2 and forgetting the middle term 2ab. Always include the cross term.
Can you verify a binomial square by multiplying?
Yes. Multiply (a + b)(a + b) using FOIL: a^2 + ab + ab + b^2 = a^2 + 2ab + b^2, confirming the formula.
Where are squares of binomials taught?
Squares of binomials are covered in the Yoshiwara Elementary Algebra textbook for Grade 6.