(x+7)(x-2)+14x

2 min read Jun 17, 2024

Simplifying the Expression (x+7)(x-2)+14x

This article will guide you through simplifying the expression (x+7)(x-2)+14x. We will use the distributive property and combining like terms to achieve a simplified form.

Step 1: Expanding the Product

First, we need to expand the product of the two binomials (x+7)(x-2). This can be done using the FOIL method:

First: x * x = x²
Outer: x * -2 = -2x
Inner: 7 * x = 7x
Last: 7 * -2 = -14

Combining these terms gives us: x² - 2x + 7x - 14

Step 2: Combining Like Terms

Now we have the expression: x² - 2x + 7x - 14 + 14x

Combining the x terms, we get: x² + 19x - 14

Final Simplified Form

The simplified form of the expression (x+7)(x-2)+14x is x² + 19x - 14.

Conclusion

By applying the distributive property and combining like terms, we were able to simplify the given expression. This process is fundamental in algebra and allows us to manipulate expressions to solve for unknown variables or understand their relationships.