How do you simplify #(-2-3sqrt5)(5-sqrt5)#?

1 Answer
NJ
Apr 1, 2018

#=>5 -13sqrt5#

Explanation:

We are given:

#(color(blue)(-2)color(red)(-3sqrt5))(color(orange)(5)color(green)(-sqrt5))#

We need to multiply the two binomials. This means we multiply each term in one binomial by each term in the other.

#=(color(blue)(-2))(color(orange)(5)) + (color(blue)(-2))(color(green)(-sqrt5)) + (color(red)(-3sqrt5))(color(orange)(5)) + (color(red)(-3sqrt5))(color(green)(-sqrt5))#

Now we simplify:

#=(-10) + (2sqrt5) + (-15sqrt5) + (3sqrt5sqrt5)#

#= -10 + 2sqrt5 - 15sqrt5 + 3(5)#

#= -10 + 2sqrt5 - 15sqrt5 + 15 #

#=5 -13sqrt5#

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