Answer:
26. (-14)
27. −4.732050808
Step-by-step explanation:
26. [tex](\sqrt{2}+4)(\sqrt{2}-4)[/tex]
Multiplication can be transformed into difference of squares using the rule:
(a − b) (a + b) = a² - b²
[tex](\sqrt{2} ^{2} ) - 4^{2}[/tex]
The square of √2 is 2.
[tex]2 - 4^{2}[/tex]
Calculate 4 to the power of 2 and get 16.
2 - 16
Subtract 16 from 2 to get −14.
-14
27. [tex](\sqrt{3} +2)(\sqrt{3} -3)[/tex]
Apply the distributive property by multiplying each term of √3 + 2 by each term of √3 - 3.
[tex]\sqrt{3} ^{2}-3\sqrt{3} +2\sqrt{3} -6[/tex]
The square of √3 is 3.
[tex]3-3\sqrt{3} +2\sqrt{3} -6[/tex]
Combine -3√3 and 2√3 to get -√3.
[tex]3-\sqrt{3} -6[/tex]
Subtract 6 from 3 to get −3.
-3 - √3
-3 - √3 ≈ −4.732050808
