To find the sum of the polynomials 7x³, 2x³, 4x², and 4x², we need to combine like terms. First, let’s identify the like terms in the given polynomials:
- 7x³ and 2x³ are like terms because they both contain the variable x raised to the same power (³).
- 4x² and 4x² are also like terms as they both contain the variable x raised to the power of ².
Now let’s perform the addition for the like terms:
- For the x³ terms: 7x³ + 2x³ = (7 + 2)x³ = 9x³
- For the x² terms: 4x² + 4x² = (4 + 4)x² = 8x²
Now, we can combine these results to write the final sum of the polynomials:
Sum: 9x³ + 8x²