Question 1051736: Multiply as indicated and simplify
(4n + 7)(n^2 - 7n - 7)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you are using the distributive law of multiplication.
the law states:
a*(b+c) = a*b + a*c
a*(b+c+d) = a*b + a*c + a*d
(a+b)*c = a*c + b*c
(a+b)*(c+d) = a*c + a*d
+ b*c + b*d
(a+b)*(c+d+e) = a*c + a*d + a*e
+ b*c + b*d + b*e
it works with negative values as well.
for example:
(a-b)*(c+d+e) = a*c + a*d + a*e
- b*c - b*d - b*e
dealing with the negatives is the hardest part.
you have to be very careful not to screw something up.
using the distributive law, i would solve your problem in the following manner:
(4n + 7)*(n^2 - 7n - 7) = 4n*n^2 + 4n*-7n + 4n*-7
+ 7*n^2 + 7*-7n + 7*-7
what you are looking at is then:
(4n + 7)*(n^2 - 7n - 7) = 4n*n^2 + 4n*-7n + 4n*-7 + 7*n^2 + 7*-7n + 7*-7
simplify this to get:
(4n + 7)*(n^2 - 7n - 7) = 4n^3 - 28n^2 -28n + 7n^2 - 49n -49
now you want to combine like terms to get:
(4n + 7)*(n^2 - 7n - 7) = 4n^3 - 21n^2 -77n -49
what's left is to confirm you did it right.
what i usually do is take a random value of the variable and then analyze both the original expression and the final expression to see that the answer is the same.
if it is, i probably did good.
if it isn't, i go back and see what i did wrong.
i will take a random value of n as 20.
i picked a nice round number to make the calculations easier.
my equation is:
(4n + 7)*(n^2 - 7n - 7) = 4n^3 - 21n^2 -77n -49
i evaluate the expression on the left of the equal sign and then i evaluate the expression on the right side of the equal side, using 20 as my value for n.
(4n + 7) * (n^2 - 7n - 7) becomes (4*20 + 7) * (20^2 - 7*20 - 7).
the result is equal to 22011
4n^3 - 21n^2 - 77n - 49 becomes 4*20^3 - 21*20^2 - 77*20 - 49.
the result is equal to 22011.
the results are the same, so i assume that i applied the distributive law to the original equation correctly.
my final expression is 4n^3 - 21n^2 -77n -49
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