Examples of squaring binomials

📚 Quick Study Guide

• ➕ A binomial is an algebraic expression with two terms, for example, $x + y$.
• 🔢 Squaring a binomial means multiplying it by itself: $(x + y)^2 = (x + y)(x + y)$.
• 🔑 The general formula for squaring a binomial $(a + b)$ is: $(a + b)^2 = a^2 + 2ab + b^2$.
• 💡 Similarly, the general formula for squaring a binomial $(a - b)$ is: $(a - b)^2 = a^2 - 2ab + b^2$.
• 📝 The key difference is the sign of the middle term ($2ab$ or $-2ab$).
• 🎯 Remember to apply the distributive property (or FOIL method) correctly.
• ✅ Always simplify your final answer by combining like terms.

Practice Quiz

1. What is the result of squaring the binomial $(x + 3)$?
   1. $x^2 + 6x + 9$
   2. $x^2 + 9$
   3. $x^2 + 3x + 9$
   4. $x^2 + 6x + 6$
2. Expand the binomial $(2y - 1)^2$.
   1. $4y^2 - 4y + 1$
   2. $4y^2 - 1$
   3. $4y^2 + 4y + 1$
   4. $2y^2 - 4y + 1$
3. What does $(a + 5)^2$ equal?
   1. $a^2 + 10a + 25$
   2. $a^2 + 25$
   3. $a^2 + 5a + 25$
   4. $a^2 + 10a + 5$
4. Simplify $(3x - 2)^2$.
   1. $9x^2 - 12x + 4$
   2. $9x^2 - 4$
   3. $9x^2 + 12x + 4$
   4. $3x^2 - 12x + 4$
5. Calculate $(x + 4)^2$.
   1. $x^2 + 8x + 16$
   2. $x^2 + 16$
   3. $x^2 + 4x + 16$
   4. $x^2 + 8x + 8$
6. What is the expansion of $(2a + 3)^2$?
   1. $4a^2 + 12a + 9$
   2. $4a^2 + 9$
   3. $4a^2 + 6a + 9$
   4. $2a^2 + 12a + 9$
7. Evaluate $(y - 6)^2$.
   1. $y^2 - 12y + 36$
   2. $y^2 - 36$
   3. $y^2 + 12y + 36$
   4. $y^2 - 6y + 36$