Question

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

Answer 1

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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