How do you simplify #(3sqrta -7)(3sqrta +7)#?

2 Answers
Aug 17, 2017

Answer:

This can be simplified to #9a-49#. See explanation.

Explanation:

If we have a product of 2 expressions with different signs we can write it as the difference of squares of the expressions.

#(a-b)xx(a+b)=a^2-b^2#

Here the squares are:

#(3sqrt(a))^2=9a#

and

#7^2=49#

Aug 17, 2017

Answer:

#color(magenta)(9a-49#

Explanation:

#(3sqrta-7)(3sqrta+7)#

#:.color(white)(aaaaa)##color(magenta)(sqrtaxxsqrta=a#

#:.color(white)(aaa)##3sqrtaxx3sqrta=9a#------------(1)

#:.color(white)(a)##color(white)(aaa)##-7xx+7=-49#--------(2)

#:.color(white)(aaaa)##-7xx3sqrta=-21sqrta#----(3)

#:.color(white)(aaaaaa)##7xx3sqrta=21sqrta#--------(4)

#color(magenta)((1)+(2)+(3)+(4)#

#:.9a-49-21sqrta+21sqrta#

#:.color(magenta)(=9a-49#