(x%5E2-7x-2).jpeg "(x-3)(x^2-7x-2)")
Expanding the Expression (x-3)(x^2-7x-2)
This article will guide you through the process of expanding the expression (x-3)(x^2-7x-2). We'll break down each step and explain the underlying concepts.
Understanding the Problem
The given expression represents the multiplication of two binomials:
- (x - 3) is a binomial with two terms, x and -3.
- (x^2 - 7x - 2) is a trinomial with three terms, x^2, -7x, and -2.
The Distributive Property
The key to expanding this expression is the distributive property. This property states that multiplying a sum by a number is the same as multiplying each term of the sum by that number.
In our case, we need to distribute each term of (x - 3) to each term of (x^2 - 7x - 2):
- x * (x^2 - 7x - 2) = x^3 - 7x^2 - 2x
- -3 * (x^2 - 7x - 2) = -3x^2 + 21x + 6
Combining Like Terms
Now, we add the results of the distributive property:
x^3 - 7x^2 - 2x - 3x^2 + 21x + 6
Combine the terms with the same powers of x:
x^3 + (-7x^2 - 3x^2) + (-2x + 21x) + 6
This simplifies to:
x^3 - 10x^2 + 19x + 6
Conclusion
Therefore, the expanded form of the expression (x-3)(x^2-7x-2) is x^3 - 10x^2 + 19x + 6.