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Salsk061 [2.6K]
2 years ago
15

Select the correct answer. Which expression is equivalent to this polynomial? x2 + 8

Mathematics
2 answers:
Svetlanka [38]2 years ago
3 0

Answer:

D ( x -2i sqrt(2)) ( x+ 2i sqrt(2))

Step-by-step explanation:

x^2 + 8

We want to factor so rewrite as squares

x^2 + (2sqrt(2))^2

Rewrite with a subtraction sign i^2 = -1

x^2 - (2*i*sqrt(2))^2

This is the difference of squares

a^2 - b^2 = ( a-b) (a+b)

( x -2i sqrt(2)) ( x+ 2i sqrt(2))

o-na [289]2 years ago
3 0

Answer:

Option D is the correct answer

Step-by-step explanation:

(x + 2 \sqrt{2} i)(x  -  2 \sqrt{2} i) \\  \\  = ( {x})^{2}  -  {(2 \sqrt{2}i )}^{2}  \\  \\  =  {x}^{2}  -  {2}^{2}. {( \sqrt{2} )}^{2}  {i}^{2}  \\  \\  =  {x}^{2}  - 4.2( - 1) \\( \because \:  {i}^{2}  =  - 1)  \\   \\ =  {x}^{2}   + 8

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