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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