(x-3)(x+7)-(x+5)(x-1)

2 min read Jun 17, 2024

Simplifying the Expression: (x-3)(x+7) - (x+5)(x-1)

This article will guide you through simplifying the expression (x-3)(x+7) - (x+5)(x-1). We'll use the distributive property and basic algebraic operations to arrive at a simplified form.

Expanding the Expressions

First, let's expand the products using the distributive property:

(x-3)(x+7) = x(x+7) - 3(x+7)
(x+5)(x-1) = x(x-1) + 5(x-1)

Now, let's distribute further:

x(x+7) - 3(x+7) = x² + 7x - 3x - 21
x(x-1) + 5(x-1) = x² - x + 5x - 5

Combining Like Terms

Let's combine like terms in both expressions:

x² + 7x - 3x - 21 = x² + 4x - 21
x² - x + 5x - 5 = x² + 4x - 5

Subtracting the Expressions

Now, we can substitute these simplified expressions back into the original equation:

(x-3)(x+7) - (x+5)(x-1) = (x² + 4x - 21) - (x² + 4x - 5)

Subtracting the second expression from the first, we get:

(x² + 4x - 21) - (x² + 4x - 5) = x² + 4x - 21 - x² - 4x + 5

Final Simplification

Finally, we can combine the like terms again:

x² + 4x - 21 - x² - 4x + 5 = -16

Therefore, the simplified expression for (x-3)(x+7) - (x+5)(x-1) is -16.