Question

How do you combine like terms in `(\frac { 34} { 7} b ^ { 3} + \frac { 9} { 7} b ^ { 4} + 7b ^ { 2} ) - ( \frac { 5} { 4} b ^ { 3} + 2b ^ { 4} + \frac { 9} { 4} b ^ { 2} )`?

Answer 1

`-5/7b^4 +101/28b^2 +19/4b^2`

Explanation:

Remove the brackets first. The negative sign will change the signs in the second bracket.

Identify the like terms:

`color(blue)(34/7b^3) +color(red)(9/7b^4) +color(green)(7b^2) color(blue)(-5/4b^3)color(red)( -2b^4)color(green)( -9/4b^2)`

`=color(red)(9/7b^4 -2b^4) color(blue)(+34/7b^3 -5/4b^3) +color(green)(7b^2-9/4b^2)`

`=color(red)(1 2/7b^4 -2b^4) +color(blue)((136b^2-35b^2)/28) +color(green)(7b^2-2 1/4b^2)`

`=color(red)(-5/7b^4) color(blue)(+101/28b^3) +color(green)(19/4b^2)`

Note the following:

• The terms are in descending powers of `b`

• Improper fractions are used - they were given

• the fractions are in simplest form