Video Transcript
Subtract negative eight 𝑥 squared 𝑦 plus two 𝑥 cubed 𝑦 cubed plus six 𝑥 to the power of four 𝑦 from negative 𝑥 to the power of four 𝑦 minus eight 𝑥 cubed 𝑦 cubed plus nine 𝑥 squared 𝑦.
As we’re subtracting the first term from the second term, it is important that we set this out in the correct order. Once we have done this, we need to collect the like terms. Remember, you can only collect like terms if the indices, or exponents, are the same. We can collect the two yellow terms, the two pink terms, and the two red terms.
Collecting the two yellow terms gives us negative 𝑥 to the power of four 𝑦 minus positive six 𝑥 to the power of four 𝑦. A negative and a positive sign becomes a negative, as when we subtract a positive number, it is the same as just subtracting the number. Negative one minus six equals negative seven. Therefore, these two terms simplify to negative seven 𝑥 to the power of four 𝑦.
Our second step is to subtract positive two 𝑥 cubed 𝑦 cubed from negative eight 𝑥 cubed 𝑦 cubed. Once again, the signs in the middle become a negative, or subtraction. Negative eight minus two is equal to negative 10. So, we’re are left with negative 10𝑥 cubed 𝑦 cubed.
Finally, we need to subtract negative eight 𝑥 squared 𝑦 from nine 𝑥 squared 𝑦. This time, our two negative signs become a positive, or addition sign. Positive nine plus eight equals 17. Therefore, our third term is 17𝑥 squared 𝑦.
This means that when we subtract negative eight 𝑥 squared 𝑦 plus two 𝑥 cubed 𝑦 cubed plus six 𝑥 to the power of four 𝑦 from negative 𝑥 to the power of four 𝑦 minus eight 𝑥 cubed 𝑦 cubed plus nine 𝑥 squared 𝑦, our answer is negative seven 𝑥 to the power of four 𝑦 minus 10𝑥 cubed 𝑦 cubed plus 17𝑥 squared 𝑦. These three terms can be written in any order. We often write the positive terms first. In this case, the 17𝑥 squared 𝑦.
