Write as an expression and simplify
a) the difference of the squares of 2m and 7n.
b)the square of the difference of x and 8y.
c)the tripled product of 6a and b^2.
d)the product of the sum of a and b and their difference.

The simplified expressions are:

a) 4m² - 49n²

b) x² - 16xy + 64y²

c) 18ab²

d) a² - b²

a) The difference of the squares of 2m and 7n:

(2m)² - (7n)²

= 4m² - 49n²

b) The square of the difference of x and 8y:

= (x - 8y)²

= x² - 16xy + 64y²

c) The tripled product of 6a and b²:

= 3(6a * b²)

= 3(6ab²)

= 18ab²

d) The product of the sum of a and b and their difference:

= (a + b)(a - b)

= a² - b²

The simplified expressions are:

a) 4m² - 49n²

b) x² - 16xy + 64y²

c) 18ab²

d) a² - b²

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Part a)

Part b)

Part c)

Part d)  

Step-by-step explanation:

Part a) The difference of the squares of 2m and 7n.

we know that

The difference of the squares formula is equal to

substitute

Part b) The square of the difference of x and 8y

The formula of the square of the difference between two numbers is equal to

substitute

Part c) The tripled product of 6a and b^2

we have

Part d) The product of the sum of a and b and their difference

The expression is equal to

The expression represent the difference of the squares between a and b

so

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!

step-by-step explanation:

ok one would be money, and the other would be refreshments or something similar. if each bag of popcorn is 5.00 and each drink is half of that that means drinks are 2.50 the proper way to do that would to look and see how much of each you can buy without exceeding a limit of 30.00