(3x+1)(x-1)+2(x^2-5)

2 min read Jun 16, 2024

Expanding and Simplifying the Expression (3x+1)(x-1)+2(x^2-5)

This article will guide you through the process of expanding and simplifying the given algebraic expression: (3x+1)(x-1)+2(x^2-5). We will use the distributive property and combine like terms to arrive at a simplified form.

Step 1: Expanding the First Product

First, we will expand the product (3x+1)(x-1) using the distributive property, also known as FOIL (First, Outer, Inner, Last):

First: (3x) * (x) = 3x^2
Outer: (3x) * (-1) = -3x
Inner: (1) * (x) = x
Last: (1) * (-1) = -1

Combining these terms, we get: 3x^2 - 3x + x - 1

Step 2: Expanding the Second Product

Next, we will expand the product 2(x^2-5) by distributing the 2:

2 * x^2 = 2x^2
2 * (-5) = -10

This gives us: 2x^2 - 10

Step 3: Combining Like Terms

Now, we combine the results from steps 1 and 2:

(3x^2 - 3x + x - 1) + (2x^2 - 10)

Combining the x^2 terms: 3x^2 + 2x^2 = 5x^2

Combining the x terms: -3x + x = -2x

Combining the constant terms: -1 - 10 = -11

Simplified Expression

Finally, we arrive at the simplified form of the expression:

(3x+1)(x-1)+2(x^2-5) = 5x^2 - 2x - 11

This expression is now in its simplest form, with all like terms combined and no further simplification possible.