How do you multiply #(sqrtt-y) (sqrtt+y) #?

1 Answer
Sep 13, 2015

Answer:

#(sqrt(t)-y)(sqrt(t)+y)= t-y^2#

Explanation:

In general we have a standard formula called the difference of squares:
#color(white)("XX")(a^2-b^2) = (a-b)(a+b)#

This can be written in reverse as
#color(white)("XX")(a-b)(a+b) = a^2-b^2#

Substituting
#color(white)("XX")sqrt(t) " for "a#
and
#color(white)("XX")y " for " b#

we have
#color(white)("XX")(sqrt(t)-y)(sqrt(t)+y)#

#color(white)("XXX")= (sqrt(t))^2-y^2#

#color(white)("XXX")=t-y^2#