Respuesta :

carlosego

For this case we must find the product of the following expression:

[tex](5 \sqrt {2} -4 \sqrt {3}) (5 \sqrt {2} -4 \sqrt {3})[/tex]

We apply distributive property that states:

[tex](a + b) (c + d) = ac + ad + bc + bd[/tex]

So:

[tex](5 \sqrt {2}) ^ 2- (5 \sqrt {2}) (4 \sqrt {3}) - (4 \sqrt {3}) (5 \sqrt {2}) + (4 \sqrt { 3}) ^ 2 =\\25 * 2-20 \sqrt {6} -20 \sqrt {6} + 16 * 3 =\\50-40 \sqrt {6} + 48 =\\98-40 \sqrt {6}[/tex]

Answer:

Option D

imlittlestar

Answer:

The correct answer is last option

98 - 40√6

Step-by-step explanation:

Identities

( a - b)(a - b) = a² - 2ab + b²

It is given that (5√2 - 4√3)(5√2 - 4√3)

To find the product 5√2 - 4√3)(5√2 - 4√3)

Using identity, we can write

(5√2 - 4√3)(5√2 - 4√3) = (5√2 - 4√3)²

(5√2 - 4√3)² = (5√2 )² - (2 * 5√2 * 4√3 ) + (4√3)²

  = (25*2) - (40 *√6) + (16 * 3)

  = 50 - 40√6 + 48

  = 98 - 40√6

The correct answer is last option 98 - 40√6

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