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