(x%2Bb)-formula-proof.jpeg "(x+a)(x+b) Formula Proof")
Proof of (x+a)(x+b) Formula
The formula for the product of two binomials, (x+a) and (x+b), is widely used in algebra and is given by:
(x+a)(x+b) = x^2 + (a+b)x + ab
In this article, we will prove this formula using the distributive property of multiplication over addition.
Step 1: Multiply the Two Binomials
To multiply the two binomials, we need to multiply each term in the first binomial by each term in the second binomial.
(x+a)(x+b) = x(x+b) + a(x+b)
Step 2: Expand the Products
Now, we expand the products using the distributive property:
x(x+b) = x^2 + xb
a(x+b) = ax + ab
Step 3: Combine Like Terms
Next, we combine like terms:
(x+a)(x+b) = x^2 + xb + ax + ab
Step 4: Simplify the Expression
Finally, we simplify the expression by combining the like terms xb and ax:
(x+a)(x+b) = x^2 + (a+b)x + ab
Thus, we have proved the formula:
(x+a)(x+b) = x^2 + (a+b)x + ab
This formula is a fundamental result in algebra and is used extensively in various mathematical operations, such as expanding quadratic expressions and solving equations.
