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wlad13 [49]
3 years ago
14

You want to frame a picture that is 5 in by 7 in with a 1 in wide frame. What is the perimeter of the outside edge of the frame?

Mathematics
1 answer:
r-ruslan [8.4K]3 years ago
4 0
94 if your using the whole frame the math is 5×7=35 we have 2 sides do times 35 by 2 35×2=70 then we do 1×7=7 for the outside of the game then do 7 times 2 b/c you have 2 sides the do your final side by doing 5×1=5 then times that by 2 and you get 10 .70+14+10=94
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{a}^{3}  + {b}^{3} = (a + b)( {a}^{2 }  - ab +  {b}^{2} )


EXPLANATION

To find the expression that is equivalent to
{a}^{3}  + {b}^{3}
we must first expand
{(a + b)}^{3}
Then we rearrange to find the required expression.


So let's get started.


{(a + b)}^{3}  = (a + b) {(a + b)}^{2}

We expand the parenthesis on the right hand side to get,



{(a + b)}^{3}  = (a + b) ( {a}^{2} + 2ab +  {b}^{2}  )



We expand again to obtain,

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Let us group the cubed terms on the right hand side to get,

{(a + b)}^{3}  =  {a}^{3}   +  {b}^{3}  + 3 {a}^{2}b + 3a {b}^{2}




{(a + b)}^{3}  =  {a}^{3}   +  {b}^{3}  + 3ab (a+ b)





We make the cubed terms the subject,

{(a + b)}^{3}  - 3ab (a+ b) =  {a}^{3}   +  {b}^{3}

We factor to get,


(a + b)({(a + b)}^{2}  - 3ab ) =  {a}^{3}   +  {b}^{3}


We expand the bracket on the left hand side to get,

(a + b)( {a}^{2}  + 2ab +  {b}^{2}   - 3ab ) =  {a}^{3}   +  {b}^{3}


We finally simplify to get,

(a + b)( {a}^{2}   - ab +  {b}^{2}  ) =  {a}^{3}   +  {b}^{3}
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