(2x+3)(x-6)-2x^2+3x+30

2 min read Jun 16, 2024

Simplifying the Expression (2x+3)(x-6)-2x^2+3x+30

This article will guide you through simplifying the expression (2x+3)(x-6)-2x^2+3x+30. We'll break down the steps and use the distributive property and combining like terms to reach the final simplified form.

Step 1: Expand the product of binomials

Start by expanding the product of the two binomials using the FOIL method:

First: 2x * x = 2x²
Outer: 2x * -6 = -12x
Inner: 3 * x = 3x
Last: 3 * -6 = -18

Therefore, (2x+3)(x-6) = 2x² - 12x + 3x -18

Step 2: Combine like terms

Let's combine the like terms within the expanded expression:

2x² - 12x + 3x - 18 = 2x² - 9x - 18

Step 3: Combine with the remaining terms

Now, bring in the remaining terms from the original expression:

2x² - 9x - 18 - 2x² + 3x + 30

Step 4: Simplify by combining like terms again

Finally, combine all the like terms:

2x² - 2x² - 9x + 3x - 18 + 30 = -6x + 12

Conclusion

Therefore, the simplified form of the expression (2x+3)(x-6)-2x² + 3x + 30 is -6x + 12. This process demonstrates the importance of understanding the order of operations, distributive property, and combining like terms when simplifying algebraic expressions.