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Add 7𝑎𝑏 − 2𝑐²𝑑² − 𝑒³𝑓² to 8𝑒³𝑓² − 9𝑐²𝑑² − 5𝑎𝑏.

Add seven 𝑎𝑏 minus two 𝑐 squared 𝑑 squared minus 𝑒 cubed 𝑓 squared to eight 𝑒 cubed 𝑓 squared minus nine 𝑐 squared 𝑑 squared minus five 𝑎𝑏.

In order to add these two expressions, we need to collect or group the like terms. Seven 𝑎𝑏 minus five 𝑎𝑏 is equal to two 𝑎𝑏. Negative two 𝑐 squared 𝑑 squared minus nine 𝑐 squared 𝑑 squared is equal to negative 11𝑐 squared 𝑑 squared, as negative two minus nine equals negative 11. Negative 𝑒 cubed 𝑓 squared plus eight 𝑒 cubed 𝑓 squared is equal to seven 𝑒 cubed 𝑓 squared, as negative one plus eight is equal to seven.

This means that our final answer is two 𝑎𝑏 minus 11𝑐 squared 𝑑 squared plus seven 𝑒 cubed 𝑓 squared. We could rewrite these three terms in any order as long as the two 𝑎𝑏 is positive, the 11𝑐 squared 𝑑 squared is negative, and the seven 𝑒 cubed 𝑓 squared is positive. For example, the answer could also be written seven 𝑒 cubed 𝑓 squared minus 11𝑐 squared 𝑑 squared plus two 𝑎𝑏.

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