## simplify expression 4ab(sqrt2b)-3a(sqrt18b^3)=7ab(sqrt6b)

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.
ashley7357
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### simplify expression 4ab(sqrt2b)-3a(sqrt18b^3)=7ab(sqrt6b)

simplify the expression 4ab(sqrt2b)-3a(sqrt18b^3)=7ab(sqrt6b)

snowdrifter
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### Re: simplify the expression

ashley7357 wrote:simplify the expression 4ab(sqrt2b)-3a(sqrt18b^3)=7ab(sqrt6b)

I assume your question is: Simplify 4ab(sqrt(2b))-3a(sqrt(18b^3))=7ab(sqrt(6b))
In that case square both sides. The left side is of the equation is complicated but if you square it using
(x - y)^2 = x^2 -2xy + y^2 you will find that for this particular question you end up with a perfect square under the root in the 2xy term. Then it is a matter of gathering like terms.

stapel_eliz
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ashley7357 wrote:simplify the expression 4ab(sqrt2b)-3a(sqrt18b^3)=7ab(sqrt6b)

The instructions say to "simplify the expression", but the "equals" sign makes this an equation...?

aeb
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### Re: simplify the expression

ashley7357 wrote:simplify the expression 4ab(sqrt2b)-3a(sqrt18b^3)=7ab(sqrt6b)

i do not unstand this please someone help ...[img] :confused

snowdrifter
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### Re: simplify the expression

To clarify, this was the question

Simplify: $4ab sqrt{2b} - 3 sqrt{18 b^3} = 7ab sqrt{6b}$

And yes, we are simplifying an equation.

The first step is: $(4ab sqrt{2b} - 3 sqrt{18 b^3})^2 = (7ab sqrt{6b})^2$

If you are careful with the algebra, you can eliminate all the radicals.

In fact, as long as b is not equal to zero you can solve this equation for a.

$a \approx -1.10778$

Which, I suppose, is as simple as it gets.