(8x^2+2x-6)-(5x^2-3x+2)

2 min read Jun 16, 2024
(8x^2+2x-6)-(5x^2-3x+2)

Simplifying the Expression: (8x^2 + 2x - 6) - (5x^2 - 3x + 2)

This problem involves simplifying an expression by subtracting two polynomials. Let's break down the steps:

1. Distribute the Negative Sign

The negative sign in front of the second parenthesis needs to be distributed to each term inside the parenthesis.

(8x^2 + 2x - 6) - (5x^2 - 3x + 2) becomes (8x^2 + 2x - 6) - 5x^2 + 3x - 2

2. Combine Like Terms

Now, we can combine the terms that have the same variable and exponent:

  • x^2 terms: 8x^2 - 5x^2 = 3x^2
  • x terms: 2x + 3x = 5x
  • Constant terms: -6 - 2 = -8

3. The Simplified Expression

Putting the combined terms together, the simplified expression is:

3x^2 + 5x - 8

Conclusion

By distributing the negative sign and combining like terms, we successfully simplified the expression (8x^2 + 2x - 6) - (5x^2 - 3x + 2) to 3x^2 + 5x - 8.

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