There are different methods to find an expression equivalent to 16m^2-40m+25, but one common one is to use the square of a binomial formula, which states that:
Step-by-step explanation:
(a - b)^2 = a^2-2ab+b^2
If we let a = 4m and b = 5/2, we can see that:
(a - b)^2 = (4m - 5/2)^2
= 16m^2-20m + (5/2)^2
= 16m^2-20m + 25/4
To get rid of the 25/4 term, we can add and subtract it from 16m^2 - 40m + 25, like this:
16m^2-40m + 25 = 16m^2 - 20m + 25/4 + 25/4-40m
= (4m - 5/2)^2 - 10m
Therefore, an expression equivalent to 16m^2-40m+25 is (4m - 5/2)^2 - 10m.
Answers & Comments
Answer:
There are different methods to find an expression equivalent to 16m^2-40m+25, but one common one is to use the square of a binomial formula, which states that:
Step-by-step explanation:
(a - b)^2 = a^2-2ab+b^2
If we let a = 4m and b = 5/2, we can see that:
(a - b)^2 = (4m - 5/2)^2
= 16m^2-20m + (5/2)^2
= 16m^2-20m + 25/4
To get rid of the 25/4 term, we can add and subtract it from 16m^2 - 40m + 25, like this:
16m^2-40m + 25 = 16m^2 - 20m + 25/4 + 25/4-40m
= (4m - 5/2)^2 - 10m
Therefore, an expression equivalent to 16m^2-40m+25 is (4m - 5/2)^2 - 10m.