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(x-5)(x+6)+(x-2)(x+1)

2 min read Jun 17, 2024
(x-5)(x+6)+(x-2)(x+1)

Expanding and Simplifying the Expression: (x-5)(x+6) + (x-2)(x+1)

This article explores how to simplify the given algebraic expression: (x-5)(x+6) + (x-2)(x+1). We will use the distributive property (also known as FOIL) to expand the expressions and then combine like terms to achieve a simplified form.

Expanding the Expression

Let's break down the problem step by step:

  1. Expand the first product: (x-5)(x+6) = x(x+6) - 5(x+6) = x² + 6x - 5x - 30 = x² + x - 30

  2. Expand the second product: (x-2)(x+1) = x(x+1) - 2(x+1) = x² + x - 2x - 2 = x² - x - 2

  3. Combine the expanded terms: (x² + x - 30) + (x² - x - 2)

  4. Combine like terms: x² + x² + x - x - 30 - 2 = 2x² - 32

Final Result

Therefore, the simplified form of the expression (x-5)(x+6) + (x-2)(x+1) is 2x² - 32.

This process demonstrates how to expand and simplify algebraic expressions involving multiple products. By applying the distributive property and combining like terms, we can arrive at a more concise and manageable form of the original expression.

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