(x+1)(x+2)(x+3) Answer

Suzhoumeite

2 min read

·

Jul 03, 2024

22

Share

Expansion of (x+1)(x+2)(x+3)

In algebra, expanding a product of binomials can be a challenging task, especially when dealing with multiple factors. In this article, we will explore the expansion of the product (x+1)(x+2)(x+3).

Step 1: Expand the first two factors

To start, let's expand the first two factors:

(x+1)(x+2) = x^2 + 3x + 2

This is a simple expansion, where we multiply each term in the first factor by each term in the second factor.

Step 2: Expand the result with the third factor

Now, let's expand the result with the third factor:

(x^2 + 3x + 2)(x+3) = ?

To do this, we'll multiply each term in the first factor by each term in the third factor:

• x^2 multiplied by x+3 gives x^3 + 3x^2
• 3x multiplied by x+3 gives 3x^2 + 9x
• 2 multiplied by x+3 gives 2x + 6

Now, let's combine like terms:

x^3 + 3x^2 + 3x^2 + 9x + 2x + 6

Simplifying the expression

Finally, let's simplify the expression by combining like terms:

= x^3 + 6x^2 + 11x + 6

And that's it! We have successfully expanded the product (x+1)(x+2)(x+3).

Final answer

The final answer is:

(x+1)(x+2)(x+3) = x^3 + 6x^2 + 11x + 6