Simplifying the Expression: (x^2+4x+8)(2x6)+(5x3)(2x10)
This article will guide you through the steps to simplify the given expression: (x^2+4x+8)(2x6)+(5x3)(2x10).
Expanding the Products
We'll begin by expanding each of the products using the distributive property (also known as FOIL):

(x^2+4x+8)(2x6):
 Multiply each term in the first set of parentheses by each term in the second set of parentheses.
 (x^2 * 2x) + (x^2 * 6) + (4x * 2x) + (4x * 6) + (8 * 2x) + (8 * 6)
 This simplifies to: 2x^3  6x^2 + 8x^2  24x + 16x  48

(5x3)(2x10):
 (5x * 2x) + (5x * 10) + (3 * 2x) + (3 * 10)
 This simplifies to: 10x^2  50x  6x + 30
Combining Like Terms
Now, let's combine the terms from both expansions:
2x^3  6x^2 + 8x^2  24x + 16x  48 + 10x^2  50x  6x + 30
Combining the x^3 terms: 2x^3
Combining the x^2 terms: 6x^2 + 8x^2 + 10x^2 = 12x^2
Combining the x terms: 24x + 16x  50x  6x = 64x
Combining the constant terms: 48 + 30 = 18
The Simplified Expression
Finally, we combine all the simplified terms to get the final expression:
2x^3 + 12x^2  64x  18