# Algebra 1

I know the answers, I just don't know how to solve it and show my work.

1. (3√6 + 5√10)^2 - 286 + 60√15

2. (2 + √10)(2 - √10) - -6

3. y = √6x-18 - x (greater then or equal to) 3

Thank you

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1. I assume you want to simplify the first two

1. (3√6 + 5√10)^2 - 286 + 60√15
You must know how to square a binomial ...
= 54 + 30√60 + 250 - 286 + 60√15
= 18 + 60√15 + 60√15
= 18 + 120√15

2. the first part is the expansion of a difference of squares pattern, you must know that

3. y = √6x-18 - x

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2. Fail. It wrote it wrong. These are the problems:

(3√6 + 5√10)^2

y = √6x-18

I solved the second one.
Here are my answers, I just need to know how to solve:

286 + 60√15

x (greater than or equal to) 3

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3. Of course, if you knew how to solve them, you would naturally know how to show your work ...

#1 As always, (a+b)^2 = a^2+2ab+b^2

(3?6 + 5?10)^2
= (3?6)^2 + 2(3?6)(5?10) + (5?10)^2
= 54 + 30?60 + 250
= 304 + 60?15

So,

(3?6 + 5?10)^2 - 286 + 60?15
= 304+60?15 - 286 + 60?15
= 18 + 120?15

#2 As always, (a+b)(a-b) = a^2-b^2

(2 + ?10)(2 - ?10) - -6
= 2^2 - (?10)^2 + 6
= 4 - 10 + 6
= 0

#3
y = ?(6x-18)
y = ?6 ?(x-3)
This is just the graph of y=?x
shifted right 3 and stretched vertically by a factor of ?6

http://www.wolframalpha.com/input/?i=%E2%88%9A(6x-18)

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4. 1.

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

so

( 3 √6 + 5 √10 ) ^ 2 = ( 3 √6 ) ^ 2 + 2 * 3 √6 * 5 √10 + ( 5 √10 ) ^ 2

( 3 √6 + 5 √10 ) ^ 2 - 286 + 60 √15 =

( 3 √6 ) ^ 2 + 2 * 3 √6 * 5 √10 + ( 5 √10 ) ^ 2 - 286 + 60 √15 =

3 ^ 2 * 6 + 6 * √6 * 5 √10 + 5 ^ 2 * 10 - 286 + 60 √15 =

9 * 6 + 30 * √6 * √10 + 25 * 10 - 286 + 60 √15 =

54 + 30 * √ ( 6 * 10 ) + 250 - 286 + 60 √15 =

18 + 30 * √60 + 60 √15 =

18 + 30 * √( 4 * 15 ) + 60 √15 =

18 + 30 * √ 4 * √15 + 60 √15 =

18 + 30 * 2 * √15 + 60 √15 =

18 + 60 √15 + 60 √15 =

18 + 120 √15 =

6 * 3 + 6 * 20 √15 =

6 ( 3 + 20 √15 )

2.

( 2 + √10 ) ( 2 - √10 ) - -6 =

( 2 + √10 ) ( 2 - √10 ) + 6

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

in this case:

( 2 + √10 ) ( 2 - √10 ) = 2 ^ 2 - ( √10 ) ^ 2 = 4 - 10 = - 6

So:

( 2 + √10 ) ( 2 - √10 ) - -6 =

( 2 + √10 ) ( 2 - √10 ) + 6 =

- 6 + 6 = 0

3.

y = √6x-18 - x (greater then or equal to) 3 doesn't make sense.

But:

√ 6 x -18 - x ≥ 3 Add 18 to both sides

√ 6 x -18 - x + 18 ≥ 3 + 18

√6 x - x ≥ 21

x ( √6 - 1 ) ≥ 21 Divide both sides by ( √6 - 1 )

x = 21 / ( √6 - 1 )

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5. As you can see from the responses here, if you want a good answer, you need to be clear on just what it is you are asking.

It is not our job to figure out what you mean -- it is your job to say it so clearly that you cannot be misunderstood!

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