Simplify (2x^4 + 7x^3 - 3x^2 + 7) - (4x^4 - 3x^3 - 5x - 20)

a. show your work and justify the steps
b. state your answer in standard form

  -2x^4 +10x^3 -3x^2 +5x +27

Step-by-step explanation:

a) Using the distributive property, we can eliminate parentheses:

  2x^4 + 7x^3 - 3x^2 + 7 - 4x^4 + 3x^3 + 5x + 20

And using the distributive property again, we can factor pairs of like terms:

  = x^4(2 -4) +x^3(7 +3) -3x^2 +5x +(7 +20)

b)

  = -2x^4 +10x^3 -3x^2 +5x +27