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(x²+5x-7) - (3x²-4x-14)

Use distribute property □
Group like terms and arrange in descending powers □
Simplify □

1 answer

Let's solve the expression step by step:

  1. Distribute Property: We need to distribute the negative sign across the second polynomial: \[ (x^2 + 5x - 7) - (3x^2 - 4x - 14) = x^2 + 5x - 7 - 3x^2 + 4x + 14 \]

  2. Group Like Terms: Now we can group the like terms together:

    • Combine the \(x^2\) terms: \(x^2 - 3x^2\)
    • Combine the \(x\) terms: \(5x + 4x\)
    • Combine the constant terms: \(-7 + 14\)

    This gives us: \[ (x^2 - 3x^2) + (5x + 4x) + (-7 + 14) \]

  3. Simplify: Now, we simplify each group:

    • \(x^2 - 3x^2 = -2x^2\)
    • \(5x + 4x = 9x\)
    • \(-7 + 14 = 7\)

    Therefore, we combine these results: \[ -2x^2 + 9x + 7 \]

So, the simplified expression is: \[ \boxed{-2x^2 + 9x + 7} \]