Answer: Choice C) ![2-\sqrt{3}-2\sqrt{2}+\sqrt{6}\\\\\\](https://tex.z-dn.net/?f=2-%5Csqrt%7B3%7D-2%5Csqrt%7B2%7D%2B%5Csqrt%7B6%7D%5C%5C%5C%5C%5C%5C)
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Work Shown:
Part 1
![\frac{2-\sqrt{8}}{4+\sqrt{12}}\\\\\\\frac{(2-\sqrt{8})(4-\sqrt{12})}{(4+\sqrt{12})(4-\sqrt{12})}\\\\\\\frac{2(4-\sqrt{12})-\sqrt{8}(4-\sqrt{12})}{(4)^2-(\sqrt{12})^2}\\\\\\\frac{8-2\sqrt{12}-4\sqrt{8}+\sqrt{8}*\sqrt{12}}{16-12}\\\\\\\frac{8-2\sqrt{12}-4\sqrt{8}+\sqrt{8*12}}{4}\\\\\\](https://tex.z-dn.net/?f=%5Cfrac%7B2-%5Csqrt%7B8%7D%7D%7B4%2B%5Csqrt%7B12%7D%7D%5C%5C%5C%5C%5C%5C%5Cfrac%7B%282-%5Csqrt%7B8%7D%29%284-%5Csqrt%7B12%7D%29%7D%7B%284%2B%5Csqrt%7B12%7D%29%284-%5Csqrt%7B12%7D%29%7D%5C%5C%5C%5C%5C%5C%5Cfrac%7B2%284-%5Csqrt%7B12%7D%29-%5Csqrt%7B8%7D%284-%5Csqrt%7B12%7D%29%7D%7B%284%29%5E2-%28%5Csqrt%7B12%7D%29%5E2%7D%5C%5C%5C%5C%5C%5C%5Cfrac%7B8-2%5Csqrt%7B12%7D-4%5Csqrt%7B8%7D%2B%5Csqrt%7B8%7D%2A%5Csqrt%7B12%7D%7D%7B16-12%7D%5C%5C%5C%5C%5C%5C%5Cfrac%7B8-2%5Csqrt%7B12%7D-4%5Csqrt%7B8%7D%2B%5Csqrt%7B8%2A12%7D%7D%7B4%7D%5C%5C%5C%5C%5C%5C)
Part 2
![\frac{8-2\sqrt{12}-4\sqrt{8}+\sqrt{96}}{4}\\\\\\\frac{8-2\sqrt{4*3}-4\sqrt{4*2}+\sqrt{16*6}}{4}\\\\\\\frac{8-2\sqrt{4}*\sqrt{3}-4\sqrt{4}*\sqrt{2}+\sqrt{16}*\sqrt{6}}{4}\\\\\\\frac{8-2*2*\sqrt{3}-4*2*\sqrt{2}+4*\sqrt{6}}{4}\\\\\\\frac{8-4*\sqrt{3}-8*\sqrt{2}+4*\sqrt{6}}{4}\\\\\\](https://tex.z-dn.net/?f=%5Cfrac%7B8-2%5Csqrt%7B12%7D-4%5Csqrt%7B8%7D%2B%5Csqrt%7B96%7D%7D%7B4%7D%5C%5C%5C%5C%5C%5C%5Cfrac%7B8-2%5Csqrt%7B4%2A3%7D-4%5Csqrt%7B4%2A2%7D%2B%5Csqrt%7B16%2A6%7D%7D%7B4%7D%5C%5C%5C%5C%5C%5C%5Cfrac%7B8-2%5Csqrt%7B4%7D%2A%5Csqrt%7B3%7D-4%5Csqrt%7B4%7D%2A%5Csqrt%7B2%7D%2B%5Csqrt%7B16%7D%2A%5Csqrt%7B6%7D%7D%7B4%7D%5C%5C%5C%5C%5C%5C%5Cfrac%7B8-2%2A2%2A%5Csqrt%7B3%7D-4%2A2%2A%5Csqrt%7B2%7D%2B4%2A%5Csqrt%7B6%7D%7D%7B4%7D%5C%5C%5C%5C%5C%5C%5Cfrac%7B8-4%2A%5Csqrt%7B3%7D-8%2A%5Csqrt%7B2%7D%2B4%2A%5Csqrt%7B6%7D%7D%7B4%7D%5C%5C%5C%5C%5C%5C)
Part 3
![\frac{8-4*\sqrt{3}-8*\sqrt{2}+4*\sqrt{6}}{4}\\\\\\\frac{4*2-4*1*\sqrt{3}-4*2*\sqrt{2}+4*\sqrt{6}}{4}\\\\\\\frac{4(2-\sqrt{3}-2\sqrt{2}+\sqrt{6})}{4}\\\\\\2-\sqrt{3}-2\sqrt{2}+\sqrt{6}\\\\\\](https://tex.z-dn.net/?f=%5Cfrac%7B8-4%2A%5Csqrt%7B3%7D-8%2A%5Csqrt%7B2%7D%2B4%2A%5Csqrt%7B6%7D%7D%7B4%7D%5C%5C%5C%5C%5C%5C%5Cfrac%7B4%2A2-4%2A1%2A%5Csqrt%7B3%7D-4%2A2%2A%5Csqrt%7B2%7D%2B4%2A%5Csqrt%7B6%7D%7D%7B4%7D%5C%5C%5C%5C%5C%5C%5Cfrac%7B4%282-%5Csqrt%7B3%7D-2%5Csqrt%7B2%7D%2B%5Csqrt%7B6%7D%29%7D%7B4%7D%5C%5C%5C%5C%5C%5C2-%5Csqrt%7B3%7D-2%5Csqrt%7B2%7D%2B%5Csqrt%7B6%7D%5C%5C%5C%5C%5C%5C)
This shows the answer is choice C.
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Explanation:
There are a lot of steps, so I broke things up into 3 sections or parts. The idea I'm applying is if the denominator is of the form
, then multiplying top and bottom by
will rationalize the denominator. This is due to the difference of squares rule (step 3 of part 1). The following step shows squaring a square root has the two cancel out.
From that point, I simplified each square root and factored to cancel out a pair of '4's.
To expand out
, we can use either the FOIL method, the box method, or the distribution property. I used the distribution property.
The total distance of the car is 227.5 miles
Step-by-step explanation:
(4r)(7r)+4r(2)-5(7r)-5(2)=28r²+8r-35r-10=28r²-27r-10
3x(3x)+3x(7)-5(3x)-5(7)=9x²+21x-15x-35=9x²+6x-35
=3h(2h²)-3h(7h)+3h(1)+2(2h)-2(7h)+2(1)
=6h³-21h²+4h²+3h-14h+2
=6h³-17h²-11h+2
Answer:
8x^2+16x+16
Step-by-step explanation:
The combined area is the sum of both expressions.
2x^2-13x+21+6x^2+29x-5
8x^2+16x+16
8(x^2+2x+2)
You're right. The multiple choice is just wrong.