WEBVTT
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Expand negative two π₯ times five π₯ cubed minus five π₯ squared.
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To expand here, weβll need to use the distributive property.
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The distributive property tells us that if weβre multiplying π times π plus π, it will be equal to multiplying π times π and then adding that to π times π.
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Letβs see how we would use that here.
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In our case, the π that weβre by multiplying by is negative two π₯.
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The π would be five times π₯ cubed and the π would be five times π₯ squared.
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To distribute our π here to multiply the π times π, weβll need to multiply negative two π₯ times five π₯ cubed.
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After that, we multiply the π term by the π term, which in our case would be multiplying negative two π₯ by five π₯ squared.
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Just to know before we do that, remember that you need to keep your signs the same.
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Weβre subtracting five π₯ squared from five π₯ cubed, so we wanna subtract here.
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Weβve now added negative two π₯ times five π₯ squared.
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In our next step, we need to multiply negative two π₯ times five π₯ cubed equals negative 10π₯ to the fourth.
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Bring down our subtraction then multiply negative two π₯ times five π₯ squared.
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When we multiply those together, we get negative 10π₯ cubed.
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But because weβre subtracting a negative, we can write addition here and then bring down our 10π₯ cubed.
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We expanded the original problem using the distributive property to come to the final answer of negative 10π₯ to the fourth plus 10π₯ cubed.