2-answer-with-solution.jpeg "(a+b)2 Answer With Solution")
(a+b)^2: Formula and Solution
The formula for (a+b)^2 is a fundamental concept in algebra and is widely used in various mathematical calculations. In this article, we will explore the formula, its solution, and provide examples to illustrate its application.
The Formula:
The formula for (a+b)^2 is:
(a+b)^2 = a^2 + 2ab + b^2
This formula is derived from the binomial theorem, which states that the square of a binomial expression can be expanded as the sum of three terms: the square of the first term, twice the product of the two terms, and the square of the second term.
The Solution:
To understand the solution, let's break down the formula into its components:
- a^2: the square of the first term (a)
- 2ab: twice the product of the two terms (a and b)
- b^2: the square of the second term (b)
When we multiply (a+b) by itself, we get:
(a+b)(a+b) = a(a+b) + b(a+b)
Expanding the right-hand side of the equation, we get:
a(a+b) = a^2 + ab b(a+b) = ab + b^2
When we add the two expressions, we get:
(a+b)^2 = a^2 + ab + ab + b^2
Combining like terms, we get the final formula:
(a+b)^2 = a^2 + 2ab + b^2
Examples:
Example 1:
Find the value of (2+3)^2 using the formula.
(2+3)^2 = 2^2 + 2(2)(3) + 3^2 (2+3)^2 = 4 + 12 + 9 (2+3)^2 = 25
Example 2:
Find the value of (x+5)^2 using the formula.
(x+5)^2 = x^2 + 2x(5) + 5^2 (x+5)^2 = x^2 + 10x + 25
Example 3:
Find the value of (3x-2)^2 using the formula.
(3x-2)^2 = (3x)^2 + 2(3x)(-2) + (-2)^2 (3x-2)^2 = 9x^2 - 12x + 4
In conclusion, the formula for (a+b)^2 is a powerful tool in algebraic calculations, and understanding its solution is essential for solving various mathematical problems.
