How do you simplify #(sqrt7+5)(sqrt7-5)#?

Question

Julia Adams · Accepted Answer

See the entire simplification process below:

To multiply and simplify these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis. #(color(red)(sqrt(7)) + color(red)(5))(color(blue)(sqrt(7)) - color(blue)(5))# becomes: #(color(red)sqrt(7) xx color(blue)(sqrt(7))) - (color(red)(sqrt(7)) xx color(blue)(5)) + (color(red)(5) xx color(blue)(sqrt(7))) - (color(red)(5) xx color(blue)(5))# #sqrt(7)^2 - 5sqrt(7) + 5sqrt(7) - 25# We can now combine like terms: #7 + (-5 + 5)sqrt(7) - 25# #7 + 0 - 25# #-18#

Julia Adams · Answer

undefined To simplify the expression (sqrt7+5)(sqrt7-5), we can use the difference of squares formula. The formula states that (a+b)(a-b) is equal to a^2 - b^2. Applying this formula to the given expression, we have (sqrt7)^2 - 5^2, which simplifies to 7 - 25, resulting in -18. Therefore, the simplified form of (sqrt7+5)(sqrt7-5) is -18.