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(sqrt[3] + 4sqrt[5])(2sqrt[3] – sqrt[5])
Applying FOIL:
sqrt[3]2sqrt[3] - sqrt[3]sqrt[5] + 4sqrt[5]2sqrt[3] - 4sqrt[5]sqrt[5]
2(3) - sqrt[15] + 8sqrt[15] - 4(5)
6 - sqrt[15] + 8sqrt[15] - 20
6 + 7sqrt[15] - 20
7sqrt[15] - 14
OR, you could factor:
7(sqrt[15]-2)
.
Divide:
[(x2 – 3x + 2)/(8x - 8)] ÷ [(x2 – 4)/(5x + 10)]
Focusing on the first term in the [], we can factor:
[(x-2)(x-1)/8(x-1)] ÷ [(x2 – 4)/(5x + 10)]
Canceling like-terms:
[(x-2)/8] ÷ [(x2 – 4)/(5x + 10)]
.
Now, focus on the second term in the [], we can factor:
[(x-2)/8] ÷ [(x–2)(x+2)/5(x+2)]
Canceling like-terms:
[(x-2)/8] ÷ [(x–2)/5]
.
Now, we can change the divide to multiplication by flipping one of the terms:
[(x-2)/8] * [5/(x–2)]
Canceling like-terms:
[1/8] * [5/1]
Resulting in:
5/8
