Simplify two 𝑎 cubed minus four 𝑎 squared minus nine plus five 𝑎 cubed minus three 𝑎 plus one.
Before we start this question, it is important to remember two things. Firstly, we can only group or collect terms with the same exponent. In this question, we can group the two 𝑎 cubed and the five 𝑎 cubed and also the negative nine and positive one.
There’s only one 𝑎 squared term and, likewise, only one 𝑎 term. Therefore, these two terms cannot be simplified.
It is also important to remember our rules when two signs are touching. If we have two positive signs, our resultant sign is an addition. A positive and a negative results in a subtraction or negative sign. And two negative signs result in a positive or addition sign.
Grouping the 𝑎 cubed terms gives us two 𝑎 cubed plus five 𝑎 cubed. As two plus five is equal to seven, two 𝑎 cubed plus five 𝑎 cubed equals seven 𝑎 cubed.
As previously mentioned, there is only one 𝑎 squared and one 𝑎 term. Therefore, negative four 𝑎 squared and negative three 𝑎 need to be in the answer.
Finally, we need to collect the numbers negative nine plus positive one. As we have two positive signs touching each other, the resultant sign is positive or addition, leaving us with negative nine plus one. This is equal to negative eight.
The simplified version of two 𝑎 cubed minus four 𝑎 squared minus nine plus five 𝑎 cubed minus three 𝑎 plus one is seven 𝑎 cubed minus four 𝑎 squared minus three 𝑎 minus eight.