(4x^3-12x^2-5)-(-8x^2+4x+3) Find The Difference

Jasonbradley

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Jun 16, 2024

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Finding the Difference: (4x^3 - 12x^2 - 5) - (-8x^2 + 4x + 3)

This problem asks us to find the difference between two polynomials. Here's how to solve it:

Understanding the Problem

The problem asks us to subtract the second polynomial (-8x^2 + 4x + 3) from the first polynomial (4x^3 - 12x^2 - 5).

Solving the Problem

1. Distribute the negative sign: Remember that subtracting a polynomial is the same as adding its negative. So, we change the signs of all the terms in the second polynomial: (4x^3 - 12x^2 - 5) + (8x^2 - 4x - 3)

2. Combine like terms: Now we combine the terms with the same variable and exponent:

   • x^3 terms: 4x^3
   • x^2 terms: -12x^2 + 8x^2 = -4x^2
   • x terms: -4x
   • Constant terms: -5 - 3 = -8

3. Write the simplified expression: 4x^3 - 4x^2 - 4x - 8

The Answer

Therefore, the difference between (4x^3 - 12x^2 - 5) and (-8x^2 + 4x + 3) is 4x^3 - 4x^2 - 4x - 8.