Question

Simplify. Write the expression such that the terms are in descending order with respect to the power of g and the variables within each term are in alphabetical order.

14g2(8g+12h−16gh2)

Answer 1

To simplify the expression 14g^2(8g + 12h - 16gh^2) and write the terms in descending order with respect to the power of g and in alphabetical order within each term, distribute 14g^2 to each term inside the parentheses, combine like terms, arrange the terms in descending order with respect to the power of g, and arrange the variables within each term in alphabetical order. The simplified expression is 112g^3 - 224g^2h^2 + 168gh^2.

Step-by-step explanation:

To simplify the expression 14g^2(8g + 12h - 16gh^2) and write the terms in descending order with respect to the power of g and in alphabetical order within each term, we can follow these steps:

1. Distribute 14g^2 to each term inside the parentheses.
2. Combine like terms.
3. Arrange the terms in descending order with respect to the power of g.
4. Arrange the variables within each term in alphabetical order.

Let's do these steps:

1. 14g^2(8g + 12h - 16gh^2) = 112g^3 + 168gh^2 - 224g^2h^2
2. The terms do not have any like terms that can be combined.
3. Arrange the terms in descending order with respect to the power of g: 112g^3 - 224g^2h^2 + 168gh^2
4. Arrange the variables within each term in alphabetical order: 112g^3 - 224g^2h^2 + 168gh^2

Therefore, the simplified expression with the terms in descending order with respect to the power of g and the variables within each term in alphabetical order is 112g^3 - 224g^2h^2 + 168gh^2.