Math, asked by akalgochu, 9 months ago

Using the standard formula expand this
(5a+3b)^2-(5a-3b)^2-60ab

Answers

Answered by pulakmath007
2

SOLUTION

TO DETERMINE

Using the standard formula expand this

 \sf{ {(5a + 3b)}^{2} -  {(5a  -  3b)}^{2} - 60ab}

FORMULA TO BE IMPLEMENTED

We are aware of the formula that

 \sf{ {a}^{2}  -  {b}^{2}   = (a + b)(a - b)}

EVALUATION

Here the given expression is

 \sf{ {(5a + 3b)}^{2} -  {(5a  -  3b)}^{2} - 60ab}

We first simplify the below

 \sf{ {(5a + 3b)}^{2} -  {(5a  -  3b)}^{2}}

   \sf{  =  \bigg[(5a + 3b )+ (5a - 3b) \bigg] \times \bigg[(5a + 3b ) -  (5a - 3b) \bigg]}

   \sf{  = (5a + 3b + 5a - 3b)  \times (5a + 3b-  5a  +  3b) }

   \sf{  =10a \times 6b }

   \sf{  =60ab }

Now the given expression

 \sf{ {(5a + 3b)}^{2} -  {(5a  -  3b)}^{2} - 60ab}

 \sf{ = 60ab - 60ab}

 = 0

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