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Math Help - Squaring numbers

  1. #1
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    Squaring numbers

    Hi,

    How is the part after the arrow arrived at?

    \begin{array}{rlc}84 \cdot 90<br />
\rightarrow 10(80 \cdot 9 + 4 \cdot 9)\end{array}
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  2. #2
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    Quote Originally Posted by Hellbent View Post
    Hi,

    How is the part after the arrow arrived at?

    \begin{array}{rlc}84 \cdot 90<br />
\rightarrow 10(80 \cdot 9 + 4 \cdot 9)\end{array}
    84*90=10[84*9]=10[(80+4)*9]=10[80*9+4*9]
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  3. #3
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    \mathrm{What\: if\ I\ wanted\ to\ try\ 83 \cdot 91?}
    Factoring doesn't work, does it?
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  4. #4
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    Quote Originally Posted by Hellbent View Post
    \mathrm{What\: if\ I\ wanted\ to\ try\ 83 \cdot 91?}
    Factoring doesn't work, does it?
    You could write it as

    (83)(91)=(80+3)(90+1)=(80)(90)+(80)(1)+(3)(90)+(3)  (1)
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  5. #5
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    Hello, Hellbent!

    \text{What if  I wanted to try } 83\cdot91\,?
    \text{Factoring doesn't work, does it?}

    Here's one way . . .

    \begin{array}{ccccccc}83\cdot91 & \Rightarrow & 83\cdot(7\!\cdot\!13) \\ \\[-3mm]<br />
& \Rightarrow & 7\cdot(83\!\cdot\!13) \\ \\[-3mm]<br />
& \Rightarrow & 7\cdot\bigg[(80+3)\!\cdot\!13\bigg] \\ \\[-3mm]<br />
& \Rightarrow & 7\cdot\bigg[80\!\cdot\!13 + 3\!\cdot\!13\bigg]<br />
\end{array}

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  6. #6
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    Quote Originally Posted by Hellbent View Post
    \mathrm{What\: if\ I\ wanted\ to\ try\ 83 \cdot 91?}
    Factoring doesn't work, does it?
    You can also use your result from (84)(90)

    (83)(91)=(84-1)(90+1)=(84)(90)+84-90

    =10[80*9+4*9]-6
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