If a(x) and b(x) are linear functions with one variable, which of the following expressions produces a quadratic function?

a) (ab)(x)
b) (a/b)(x)
c) (a-b)(x)
d) (a+b)(x)

answer !

Option A (ab)(x) will form the quadratic equation.

Step-by-step explanation:

We have been given that a(x) and b(x) are linear function so we can assume

a(x)= cx+d  and b(x) = ex+f  substituting these values in the given options

In case A let us substitute the values a(x)= cx+d  and b(x) = ex+f  we will get

after simplification we will get

This is a quadratic equation because the degree of this equation is 2.

In case B let us substitute the values a(x)= cx+d  and b(x) = ex+f  we will get

which is itself a simplified from and degree in this case is 1.

Hence, this is not the quadratic equation.

In case C let us substitute the values a(x)= cx+d  and b(x) = ex+f  we will get

after simplification we will get

This is again not a quadratic equation since, degree in this case is 1.

In case D let us substitute the values a(x)= cx+d  and b(x) = ex+f  we will get

after simplification we will get

This is again not a quadratic equation since, degree in this case is 1.

Therefore, Option A (ab)(x) will form the quadratic equation.

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

it has the same slope and a different y-intercept

hope this : )