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Expand 𝑥 plus three multiplied by 𝑥 plus two squared.
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Give your answer in its simplest form.
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𝑥 plus two all squared can be rewritten as 𝑥 plus two multiplied by 𝑥 plus two.
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We can expand or multiply out these two brackets using the FOIL method.
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Multiplying the first terms, 𝑥 multiplied by 𝑥, gives us 𝑥 squared.
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Multiplying the outside terms, 𝑥 multiplied by two, is two 𝑥.
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Multiplying the inside terms also gives us two 𝑥.
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And finally, multiplying the last terms gives us plus four.
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Two multiplied by two is four.
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Grouping or simplifying the like terms gives us 𝑥 squared plus four 𝑥 plus four.
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This means that 𝑥 plus two multiplied by 𝑥 plus two or 𝑥 plus two all squared is equal to 𝑥 squared plus four 𝑥 plus four.
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Our next step is to multiply all three of these terms by 𝑥 and then all three of the terms by three.
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𝑥 multiplied by 𝑥 squared is 𝑥 cubed, 𝑥 multiplied by four 𝑥 is four 𝑥 squared, and 𝑥 multiplied by four is four 𝑥.
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We then need to multiply all three terms in the second bracket by three.
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Three multiplied by 𝑥 squared is three 𝑥 squared, three multiplied by four 𝑥 is 12𝑥, and three multiplied by four is equal to 12.
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We can simplify this by grouping the 𝑥 squared terms — four 𝑥 squared and three 𝑥 squared — and the two 𝑥 terms — four 𝑥 and 12𝑥.
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Simplifying this gives us an answer of 𝑥 cubed plus seven 𝑥 squared plus 16𝑥 plus 12.
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The expansion of 𝑥 plus three multiplied by 𝑥 plus two all squared in its simplest form is 𝑥 cubed plus seven 𝑥 squared plus 16𝑥 plus 12.