Question

How do you combine like terms in `(5.4q ^ { 4} - 2.5q ^ { 3} + 7.5q + 3) - ( 6.7q ^ { 4} + 1.7q ^ { 3} + 1.6q - 7.8)`?

Answer 1

See the entire solution process below:

Explanation:

First, remove all of the terms from parenthesis. Be careful to handle the signs of each individual term correctly:

`5.4q^4 - 2.5q^3 + 7.5q + 3 - 6.7q^4 - 1.7q^3 - 1.6q + 7.8`

Next, group like terms:

`5.4q^4 - 6.7q^4 - 2.5q^3 - 1.7q^3 + 7.5q - 1.6q + 3 + 7.8`

Now, combine like terms:

`(5.4 - 6.7)q^4 + (-2.5 - 1.7)q^3 + (7.5 - 1.6)q + (3 + 7.8)`

`-1.3q^4 + (-4.2)q^3 + 5.9q + 10.8`

`-1.3q^4 - 4.2q^3 + 5.9q + 10.8`

Answer 2

`-1.3q^4-4.2q^3+5.9q+10.8`

Explanation:

`(5.4q ^ { 4} - 2.5q ^ { 3} + 7.5q + 3) - ( 6.7q ^ { 4} + 1.7q ^ { 3} + 1.6q - 7.8)`

Everything in the first parenthesis stays the same

`5.4q ^ { 4} - 2.5q ^ { 3} + 7.5q + 3 - ( 6.7q ^ { 4} + 1.7q ^ { 3} + 1.6q - 7.8)`

All of the terms in the second parenthesis have their signs changed due to the negative outside of the parenthesis

`5.4q ^ { 4} - 2.5q ^ { 3} + 7.5q + 3- 6.7q ^ { 4} - 1.7q ^ { 3} - 1.6q + 7.8`

Add and subtract common terms

`color(red)(5.4q ^ { 4}) color(green)(- 2.5q ^ { 3}) color(blue)(+ 7.5q) + 3color(red)(- 6.7q ^ { 4})color(green)( - 1.7q ^ { 3}) color(blue)(- 1.6q) + 7.8`

`color(red)(-1.3q^4)color(green)(-4.2q^3)color(blue)(+5.9q)+10.8`

Terms are combined.

`-1.3q^4-4.2q^3+5.9q+10.8`