WEBVTT
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Find π΄π΅ given π΄ equals five π₯ cubed minus three π₯ and π΅ equals negative six π₯ squared plus three π₯.
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π΄π΅ would be multiplying the expression of π΄ and the expression of π΅.
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We need to multiply five π₯ cubed minus three π₯ times negative six π₯ squared plus three π₯.
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We do that by foiling.
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Multiplying the firsts, the outers, the inners, and the lasts.
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The first, five π₯ cubed times negative six π₯ squared.
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And then, five π₯ cubed times three π₯.
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So weβll add five π₯ cubed times three π₯.
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We need to be careful here.
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Weβre multiplying negative three π₯ by negative six π₯ squared.
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That means weβll be adding negative three π₯ times negative six π₯ squared and then negative three π₯ times positive three π₯.
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So weβll add negative three π₯ times positive three π₯.
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Five times negative six equals negative 30.
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We bring down the variable and then add the two exponents.
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Three plus two is five.
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Five π₯ cubed times negative six π₯ squared equals negative 30π₯ to the fifth.
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Follow the same procedure.
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Multiply the coefficients.
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Five times three equals 15.
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Bring down the π₯.
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Three π₯ is the same thing as three times π₯ to the first power.
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And three plus one is four.
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Five π₯ cubed times three π₯ equals 15π₯ to the fourth.
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The next term, weβll multiply negative three times negative six, which is positive 18.
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And then, weβll add the exponents of the two π₯s.
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One plus two is three.
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The last term has negative three times positive three, which is negative nine.
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Both of these π₯-values have an exponent of one.
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π₯ times π₯ is the same thing as π₯ to the one plus one power.
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Itβs π₯ squared.
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Weβre adding all these terms together, negative 30π₯ to the fifth plus 15π₯ to the fourth plus 18π₯ cubed.
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For the last term, weβre adding a negative.
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And we can simplify that by saying subtracting nine π₯ squared.
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π΄π΅ equals negative 30π₯ to the fifth plus 15π₯ to the fourth plus 18π₯ cubed minus nine π₯ squared.