How do you simplify #(3+ 2c ) ( 7- 4c )#?

Question

Isaiah Anthony · Accepted Answer

See a solution process below:

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis. #(color(red)(3) + color(red)(2c))(color(blue)(7) - color(blue)(4c))# becomes: #(color(red)(3) xx color(blue)(7)) - (color(red)(3) xx color(blue)(4c)) + (color(red)(2c) xx color(blue)(7)) - (color(red)(2c) xx color(blue)(4c))# #21 - 12c + 14c - 8c^2# We can now combine like terms: #21 + (-12 + 14)c - 8c^2# #21 + 2c - 8c^2# Or in standard form: #-8c^2 + 2c + 21#

Ethan Adkins · Answer

#21+2c-8c^2# #"simplify means to multiply the factors together"# #"each term in the second factor is multiplied by each term"# #"in the first factor"# #rArr(color(red)(3+2c))(7-4c)# #=color(red)(3)(7-4c)color(red)(+2c)(7-4c)# #"distributing the brackets gives"# #=(color(red)(3)xx7)+(color(red)(3)xx-4c)+(color(red)(2c)xx7)+(color(red)(2c)xx-4c)# #=21+(-12c)+14c+(-8c^2)# #=21+2c-8c^2#

Savannah Anderson · Answer

undefined To simplify (3 + 2c)(7 - 4c), you use the distributive property and FOIL method:

(3 + 2c)(7 - 4c) = 3 * 7 + 3 * (-4c) + 2c * 7 + 2c * (-4c)
                = 21 - 12c + 14c - 8c^2
                = 21 + 2c - 8c^2