Chapter 8.1, Problem 2P

To determine

Tosimplify:The given expressions as the sum and difference of two polynomials.

Answer to Problem 2P

The sum $-6x^4+11x^4=5x^4$ , and the difference $2x^2{y}^4-7x^2{y}^4=-5x^2{y}^4$ .

Explanation of Solution

Given information:

The given expressions are $-6x^4+11x^4$ and $2x^2{y}^4-7x^2{y}^4$ .

Conceptused:

The sum and difference of two or more polynomial is calculated by adding or subtracting the coefficients of like powers of variables.

Calculations:

The expression $-6x^4+11x^4$ is the sum of two polynomials $-6x^4$ and $11x^4$ each has 4 as the like power of variable x .

Hence, sum of $-6x^4$ and $11x^4$ is $\left(-6+11\right)x^4=5x^4$ .

Thus, the sum $-6x^4+11x^4=5x^4$ .

The expression $2x^2{y}^4-7x^2{y}^4$ is the difference of two polynomials $2x^2{y}^4$ and $7x^2{y}^4$ each has 2 as the like power of variable x and 4 as the like power of variabley.

Hence, difference of $2x^2{y}^4$ and $7x^2{y}^4$ is $\left(2-7\right)x^2{y}^4=-5x^2{y}^4$ .

Thus, the difference $2x^2{y}^4-7x^2{y}^4=-5x^2{y}^4$ .

Conclusion:

The sum $-6x^4+11x^4=5x^4$ , and the difference $2x^2{y}^4-7x^2{y}^4=-5x^2{y}^4$ .