How do you simplify $2 {(\sqrt{5 x} - 3)}^{2}$ $2(sqrt(5x) - 3)^2$ ?

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Answer 1 · 2017-04-16T04:33:48

$10 x - 12 \sqrt{5 x} + 18$ $10x-12sqrt(5x)+18$

We can rewrite the expression to specifically show all the terms:

$2 {(\sqrt{5 x} - 3)}^{2} = 2 (\sqrt{5 x} - 3) (\sqrt{5 x} - 3)$ $2(sqrt(5x)-3)^2=2(sqrt(5x)-3)(sqrt(5x)-3)$

Let's set aside the leading 2 for a minute and work with the two bracketed terms. We'll use FOIL to handle it:

FOIL

$F$ $color(red)(F)$ - First terms - $(a + b) (c + d)$ $(color(red)(a)+b)(color(red)(c)+d)$
$O$ $color(brown)(O)$ - Outside terms - $(a + b) (c + d)$ $(color(brown)(a)+b)(c+color(brown)d)$
$I$ $color(blue)(I)$ - Inside terms - $(a + b) (c + d)$ $(a+color(blue)b)(color(blue)(c)+d)$
$L$ $color(green)(L)$ - Last terms - $(a + b) (c + d)$ $(a+color(green)b)(c+color(green)d)$

This gives us:

$F \Rightarrow \sqrt{5 x} \sqrt{5 x} = 5 x$ $color(red)(F)=>sqrt(5x)sqrt(5x)=5x$
$O \Rightarrow \sqrt{5 x} (- 3) = - 3 \sqrt{5 x}$ $color(brown)(O)=>sqrt(5x)(-3)=-3sqrt(5x)$
$I \Rightarrow (- 3) (\sqrt{5 x}) = - 3 \sqrt{5 x}$ $color(blue)(I)=>(-3)(sqrt(5x))=-3sqrt(5x)$
$L \Rightarrow (- 3) (- 3) = 9$ $color(green)(L)=>(-3)(-3)=9$

$5 x - 3 \sqrt{5 x} - 3 \sqrt{5 x} + 9 = 5 x - 6 \sqrt{5 x} + 9$ $5x-3sqrt(5x)-3sqrt(5x)+9=5x-6sqrt(5x)+9$

And so $2 {(\sqrt{5 x} - 3)}^{2} = 2 (5 x - 6 \sqrt{5 x} + 9)$ $2(sqrt(5x)-3)^2=2(5x-6sqrt(5x)+9)$

We can now distribute the 2 through the bracket:

$2(5x-6sqrt(5x)+9)=color(blue)(ul(bar(abs(color(black)(10x-12sqrt(5x)+18))))$

How do you simplify 2(sqrt(5x) - 3)^22(√5x−3)22(sqrt(5x) - 3)^2?