(a-b)-formula-proof.jpeg "(a+b)(a-b) Formula Proof")
Proof of the Formula: (a+b)(a-b)
The formula (a+b)(a-b) is a well-known identity in algebra, which is widely used in various mathematical operations. In this article, we will provide a step-by-step proof of this formula.
The Formula:
The formula (a+b)(a-b) is a product of two binomials, where a and b are variables or constants.
(a+b)(a-b) = ?
To proof this formula, we will start by multiplying the two binomials using the distributive property of multiplication over addition.
(a+b)(a-b) = a(a-b) + b(a-b)
Now, we will expand the right-hand side of the equation by multiplying each term in the first binomial with each term in the second binomial.
a(a-b) = a^2 - ab
b(a-b) = ab - b^2
Now, we will combine like terms:
(a+b)(a-b) = a^2 - ab + ab - b^2
Simplifying the equation, we get:
(a+b)(a-b) = a^2 - b^2
Therefore, we have proved that:
(a+b)(a-b) = a^2 - b^2
This formula is a fundamental identity in algebra, which is used in various mathematical operations, such as factoring, solving quadratic equations, and simplifying expressions.
Conclusion:
In this article, we have provided a step-by-step proof of the formula (a+b)(a-b) = a^2 - b^2. This formula is an essential tool in algebra, and its proof is a fundamental concept in mathematics.
