WEBVTT
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Expand and simplify π₯ minus two times π₯ plus three.
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Letβs consider two different methods: first, the FOIL method; and then weβll use the grid.
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The FOIL method gives us order to our expansion, multiplying your firsts then your outers then multiplying your inner terms and then finally multiplying your last terms.
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Back to our firsts, we multiply π₯ times π₯; the outers, π₯ times three.
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Remember that weβre adding each of these terms that we multiply together.
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Inners, negative two times π₯.
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Well it is also true to subtract two times π₯ here, keeping the negative with the whole number two prevents sign mistakes later on.
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Our lasts is multiplying negative two by three.
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Our next step is to multiply: π₯ times π₯ equals π₯ squared; π₯ times three equals three π₯; negative two times π₯ equals negative two π₯; negative two times three equals negative six.
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Weβre finished FOILing and multiplying, and weβre ready to simplify.
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We simplify this by combining any like terms.
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We only have one π₯ squared term, so we bring it down.
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We have two π₯ terms, two terms that have π₯ to the first power.
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We can combine them: three π₯ plus negative two π₯ equals π₯.
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We also have a constant: a negative six.
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Itβs our only constant; there is nothing to combine it with, so we bring it down.
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And weβve found the expanded and simplified form to be π₯ squared plus π₯ minus six.
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Letβs look at another method for solving this problem.
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For the grid method, weβll take π₯ minus two and place π₯ in our first box, negative two just below it.
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Weβll then take π₯ plus three and add the π₯ to a box in the top row and the positive three to the right of it.
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And then weβll multiply.
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In the second row second column, we would multiply π₯ times π₯ which equals π₯ squared.
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The next box would be equal to π₯ times three which equals three π₯.
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After that we multiply π₯ times negative two, which equals negative two π₯.
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And then our final box, negative two times three equals negative six.
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And then we combine all four of these terms.
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π₯ squared plus three π₯ plus negative two π₯ plus negative six.
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Weβll combine like terms to simplify.
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There is nothing for us to add to π₯ squared.
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We can combine three π₯ and negative two π₯, which equals positive π₯.
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Thereβs nothing to combine the negative six with, so we bring it down.
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Both methods show the simplified form of π₯ minus two times π₯ plus three to be π₯ squared plus π₯ minus six.