(x%2B6).jpeg "(x^2-7x+12)(x+6)")
Expanding the Expression: (x^2-7x+12)(x+6)
This article will guide you through the process of expanding the given expression: (x^2-7x+12)(x+6). This involves multiplying two polynomials together, which can be done using the distributive property.
The Distributive Property
The distributive property states that for any numbers a, b, and c:
a(b + c) = ab + ac
We can extend this to multiplying two binomials:
(a + b)(c + d) = a(c + d) + b(c + d)
Applying the Distributive Property
Let's apply this to our expression:
(x^2-7x+12)(x+6) = x^2(x+6) - 7x(x+6) + 12(x+6)
Now, we can distribute each term:
= x^3 + 6x^2 - 7x^2 - 42x + 12x + 72
Combining Like Terms
Finally, we combine the like terms to simplify the expression:
= x^3 - x^2 - 30x + 72
Conclusion
Therefore, the expanded form of (x^2-7x+12)(x+6) is x^3 - x^2 - 30x + 72.
This process demonstrates the power of the distributive property in simplifying expressions involving polynomials. You can use this same method to expand any expression involving the product of two or more polynomials.