Problem Solving Made Easy (8th Grade)#4: How to find the Square of a Binomial?

_{(How to find the Square of a Binomial)}

"Solving math problem the easier way is intended to help students discover that learning math is easy. Be inspired and motivated with the hope it can sway them from having neutral opinions about math to liking it."

Hello steemian friends! Today's post discusses the steps on " How to find the Square of a Binomial " following a pattern. Again, I made it sure that the language used in the presentation is user-friendly in the sense that it is easily understood by a reader who has at least an 8th-grade education (age 13-14).

Binomial - brief review

---

A binomial is a type of a polynomial (an algebraic expression whose variables have non-negative integer exponents) with exactly two terms

To do the task, it is important to recall how to multiply polynomials particularly the product rule.

Grade 7 students in my country, Philippines, as I am not familiar as to how advanced students in other parts of the globe are, were thought how to find the product of binomials by the used of FOIL METHOD which is sometimes tedious. Here, it is assumed that the reader has already good knowledge on how to do it.

Amazingly! There are forms of algebraic expressions whose product is special (commonly called " Special Product." ) In which an apparent pattern made it special since it will make their product readily seen.

How to find the Square of a Binomial ?

---

Let ( a + b )² be the sample binomial where:

Here are the steps:

• Step 1. Square the first term
• Step 2. Twice the product of the first and the last term.
• Step 3. Square the last term.

Putting them together, the pattern would be

Application:

---

Problem: Find the square of the binomial

Solution:

• Step 1. Square the first term

• Step 2. Twice the product of the first and last term

• Step 3. Square of the last term.

Conclusion:

Therefore putting them together we have

Note: Pattern varies according to the operation used. Like if it is the square of the difference between the first and the last term (a-b)², then the pattern to be used will also be changed into (a-b)² = a² - 2ab + b²

So we're done! That's how we find the square of a binomial (a+b)². Thanks for learning with me. Steem on!

---

References:

• Wiki on Polynomial
• Wiki on Binomial
• Textbook: Advanced Algebra, Trigonometry and Statistics
  
  Images were all created by me. Thanks to MS Word and Paint.

---

"We live and learn, at any rate we live"