(3sqrt2 + sqrt5)(sqrt2 - 3sqrt(5r))(3√2+√5)(√2−3√5r)
To simplify this, we will use the distributive method called FOIL:
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Following this image, we can multiply it out.
The color(teal)("firsts")firsts:
color(teal)(3sqrt2 * sqrt2) = 3sqrt4 = 3*2 = 63√2⋅√2=3√4=3⋅2=6
The color(indigo)("outers")outers:
color(indigo)(3sqrt2 * -3sqrt(5r)) = 3 * -3 * sqrt(2 * 5r) = -9sqrt(10r)3√2⋅−3√5r=3⋅−3⋅√2⋅5r=−9√10r
The color(peru)"inners"inners:
color(peru)(sqrt5 * sqrt2) = sqrt(5*2) = sqrt10√5⋅√2=√5⋅2=√10
The color(olivedrab)"lasts"lasts:
color(olivedrab)(sqrt5 * -3sqrt(5r)) = -3sqrt(5*5r) = -3sqrt(25r) = -3*5sqrtr = -15sqrtr√5⋅−3√5r=−3√5⋅5r=−3√25r=−3⋅5√r=−15√r
Combine them all together to get your answer:
6 - 9sqrt(10r) + sqrt10 - 15sqrt(r)6−9√10r+√10−15√r
Hope this helps!
