Education

Learning Algebraic Formula | The Formula of (a-b)²

Chloe Daniel
Published On: July 14 ,2021

The algebra formula, (a-b)^2, is used to calculate the square of a binomial. It is also called the formula used to calculate the square of the difference of 2 identities or terms. We have covered the formula and a solved example for your better understanding of the formula of (a-b)². So, let’s dive in:

Algebra Formula: (a-b)^2 Proof

Now, the formula is:

(a－b)²＝a²－2ab＋b²

But if you are not sure about it, here is how you can prove it:

(a－b)²＝(a－b)(a－b)

⇒ a(a－b)－b(a－b)

⇒ a²－ab－ab＋b²

⇒ a²－2ab＋b²

Other Formulae That You Should Know Of

(a+b)^2

𝑎2 + 2𝑎𝑏 + 𝑏2

Perimeter of Parallelogram

P=2(a+b)

A Solved Example

Find out the value of (2a – 3b)2

Solution

(2a – 3b)2 = (2a)2 + (3b)2 – 2(2a)(3b)

= 4a2 + 9b2 – 2(2a)(3b)

= 4a2 + 9b2 – 12ab

Therefore,

(3a – 2b)2 = 4a2 + 9b2 – 12ab

And that’s the formula of (a-b)², explained and solved, for you.

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Chloe Daniel

Chloe has spent more than 10 years as a teacher trainer, which has given her a strong understanding of both education and the everyday challenges students face. She enjoys writing blogs that go beyond academics, covering different parts of student life while staying connected to real educational values. Her writing is simple, thoughtful, and meant to genuinely help students. Whether it’s understanding their studies better or managing their personal well-being. If you have any ideas or suggestions, feel free to reach out at chloedaniel402 [at] gmail.com.