(x^2+4x+8)(2x-6)+(5x-3)(2x-10)

2 min read Jun 17, 2024

Simplifying the Expression: (x^2+4x+8)(2x-6)+(5x-3)(2x-10)

This article will guide you through the steps to simplify the given expression: (x^2+4x+8)(2x-6)+(5x-3)(2x-10).

We'll begin by expanding each of the products using the distributive property (also known as FOIL):

(x^2+4x+8)(2x-6):
- 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
(5x-3)(2x-10):
- (5x * 2x) + (5x * -10) + (-3 * 2x) + (-3 * -10)
- This simplifies to: 10x^2 - 50x - 6x + 30

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

Finally, we combine all the simplified terms to get the final expression:

2x^3 + 12x^2 - 64x - 18