Simplify (2x^4+7x^3-3x+7)-(5x^4-4x^3-8x^2-18). Show Your Work And Explain The Steps. Leave Your Answer In Standard Form.

Simplify (2x^4+7x^3-3x+7)-(5x^4-4x^3-8x^2-18). Show your work and explain the steps. Leave your answer in standard form.

 

Answer:

Step-by-step explanation:

In subtraction we should always remember that we will do KCC (keep, change, change):

Keep all the signs of the minuend. Change subtraction sign to plus sign. Then change also all the signs of the minuend.

Follow the steps:

   2x^4+7x^3-3x+7                          2x^4+7x^3 + 0x^2-3x+7

-   5x^4-4x^3-8x^2-18             +    - 5x^4 +4x^3+8x^2+0x +18        

             

         2x^4+7x^3 + 0x^2-3x+7    

+    - 5x^4 +4x^3+8x^2+0x +18          

        -3x^4 + 11x^3+8x^2 - 3x+25

The final answer is  -3x^4 + 11x^3+8x^2 - 3x+25.

Note: If you want to have your first term to be positive then change all the signs of the term that follows:  3x^4 - 11x^3 - 8x^2 + 3x - 25