(3x^2-x-7)-(5x^2-4x-2)+(x+3)(x+2)

Jasonbradley

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Jun 16, 2024

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Simplifying Polynomial Expressions

This article will guide you through simplifying the polynomial expression: (3x^2 - x - 7) - (5x^2 - 4x - 2) + (x + 3)(x + 2).

Step 1: Distribute the Multiplication

First, we need to distribute the multiplication in the last term:

(x + 3)(x + 2) = x(x + 2) + 3(x + 2) = x^2 + 2x + 3x + 6 = x^2 + 5x + 6

Step 2: Distribute the Negative Signs

Now, we can distribute the negative signs in front of the parentheses:

(3x^2 - x - 7) - (5x^2 - 4x - 2) + (x^2 + 5x + 6) = 3x^2 - x - 7 - 5x^2 + 4x + 2 + x^2 + 5x + 6

Step 3: Combine Like Terms

Finally, we combine the like terms:

(3x^2 - 5x^2 + x^2) + (-x + 4x + 5x) + (-7 + 2 + 6) = -x^2 + 8x + 1

Conclusion

Therefore, the simplified form of the polynomial expression (3x^2 - x - 7) - (5x^2 - 4x - 2) + (x + 3)(x + 2) is -x^2 + 8x + 1.