Hey Guys!!! Are you searching various websites to know more about the expansion of powers of binomial expressions? Then you can stop your search now because this page is the one-stop solution for all the students to clarify their doubts on expansions of powers of binomials and trinomials. An algebraic expression with two constant terms is known as binomial expression. The Expansion of (a ± b)^2 is the power of the sum of two terms a and b. The square of the expansion of (a + b)^2 can be written as a² + 2ab + b² and (a – b)^2 can be written as a² – 2ab + b².
Expansion of (a ± b)^2 – Definition
The square of the sum or difference of two terms a and b are used as formulas in maths. The square of the sum of the difference of the terms a and b is expanded as the addition of two times the product of two terms from the addition of the squares of the constant terms. squared difference of two constant terms a and b is expanded as the difference of two times multiplication of two terms from the sum of the square of the terms.
(a + b)² = a² + b² + 2ab
(a – b)² = a² + b² – 2ab
How to Expand (a ± b)²?
- First, we have to go through the pattern of the given problem.
- Next, write the formula that is related to the given question.
- Now substitute the values in the formula and expand the given binomial expression.
Expansion of (a ± b)^2 Examples with Answers
Go through the below examples to know how to expand (a ± b)².
Example 1.
Expand (4a + 3b)²
Solution:
Given that
(4a + 3b)²
It is in the form of (a + b)²
We know that,
(a + b)² = a² + b² + 2ab
(4a)² + 2 × 4a × 3b + (3b)²
16a² + 24ab + 9b²
Example 2.
Expand (2m – n)²
Solution:
Given that
(2m – n)²
It is in the form of (a – b)²
We know that,
(a – b)² = a² + b² – 2ab
(2m)² – 2 × 2m × n + n²
4m² – 4mn + n²
Example 3.
Expand (3a + 1/3a)²
Solution:
Given that
(3a + 1/3a)²
It is in the form of (a + b)²
We know that,
(a + b)² = a² + b² + 2ab
(3a)² + 2 × 3p × 1/3p + (1/3p)²
9a² + 2 + (1/9p²)
Example 4.
Simplify (8m + 2n)² + (8m – 2n)²
Solution:
Given that
(8m + 2n)² + (8m – 2n)²
We know that
(a + b)² + (a – b)² = 2(a² + b²)
2{(8m)² + (2n)²}
2(84m² + 4n²)
128m² + 8n²
Example 5.
If a + 1/a = 5, find a² + 1/a²
Solution:
Given that
a² + 1/a²
We know that
x² + y² = (x + y)² – 2xy
Therefore a² + 1/a²
(a + 1/a)² – 2 × a × a × 1/a
5² – 2
25 – 2 = 23
FAQs on Expansion of (a ± b)²
1. What is the formula of (a + b)²?
The formula for (a + b)² is a² + b² + 2ab.
2. What is the formula of (a – b)²?
The formula for (a – b)² is a² + b² – 2ab.
3. How To Use the (a + b)² Formula?
i. First we have to observe the operation of the numbers whether they have the whole square or not.
ii. Next we have to apply the formula as per the arithematic operation.
iii. Substitute the values in the formula and simplify them.