Respuesta :

Given Equation

[tex] \boxed{ \tt \: (8 \sqrt{3} - 2 \sqrt{2} )(8 \sqrt{3} + 2 \sqrt{2})}[/tex]

Step by step expansion:

[tex] \dashrightarrow \sf \: (8 \sqrt{3} - 2 \sqrt{2} )(8 \sqrt{3} + 2 \sqrt{2})[/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow \sf \: (8 \sqrt{3})^{2} - (2 \sqrt{2} {)}^{2} [/tex]

Reason:

(a + b)(a - b) = a²- b²

[tex] \\ \\ [/tex]

[tex] \dashrightarrow \sf \: (8 {}^{2} \times { \sqrt{3} }^{2} )- (2 \sqrt{2} {)}^{2} [/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow \sf \: (64 \times 3 ) - (2 \sqrt{2} {)}^{2} [/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow \sf \: (64 \times 3 ) - (2 {}^{2} \times \sqrt{2} {}^{2} {)}[/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow \sf \: 192- 8[/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow \sf \: 184[/tex]

[tex] \\ \\ [/tex]

~BrainlyVIP ♡

Using subtraction of perfect squares, it is found that the result of the expression is of 184.

What is subtraction of perfect squares?

It is represented by the following identity:

[tex](a - b)(a + b) = a^2 - b^2[/tex]

In this problem, the expression is:

[tex](8\sqrt{3} - 2\sqrt{2})(8\sqrt{3} + 2\sqrt{2})[/tex]

Hence, applying the identity:

[tex](8\sqrt{3} - 2\sqrt{2})(8\sqrt{3} + 2\sqrt{2}) = (8\sqrt{3})^2 - (2\sqrt{2})^2 = 64(3) - 4(2) = 192 - 8 = 184[/tex]

Hence, the result of the expression is of 184.

To learn more about subtraction of perfect squares, you can take a look at  https://brainly.com/question/16948935

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