Question

If m(x) = x2 + 3 and n(x) = 5x + 9, which expression is equivalent to (mn)(x)?

Answer 1

It is given that,

`m(x)=x^2 +3, n(x)=5 x +9\\\\ mn(x)= (x^2+3)(5 x +9)\\\\ m n (x)=x^2* (5 x +9)+3* (5 x +9)\\\\ m n(x)=x^2 * 5 x+x^2* 9+3 * 5 x +3 * 9 \\\\m n(x)=5 x^3+9 x^2+15 x +27`

The equivalent expression to m n(x) is:

`1. x(5 x^2+9 x+15)+27\\\\ 2. 5 x^3+3 * (3 x^2+5x +9) \\\\ 3.5 x^3 +3 x* (3x +5)+27`

The Identity used here is

1. Distributive property of multiplication with respect to addition

a × (b+c)= a × b + a × c

2. Law of indices

`a^m * a^n=a^(m+n)`

Answer 2

For this case we have the following functions:

`m (x) = x ^ 2 + 3 n (x) = 5x + 9`
Multiplying both functions, we obtain an expression equivalent to (mn) (x).
We have then:

`(mn) (x) = m (x) n (x)`
Substituting values we have:

`(mn) (x) = (x ^ 2 + 3) (5x + 9)`
Rewriting the expression we have:

`(mn) (x) = (5x ^ 3 + 15x) + (9x ^ 2 + 27) (mn) (x) = 5x ^ 3 + 9x ^ 2 + 15x + 27`
Answer:
An expression that is equivalent to (mn) (x) is:

`(mn) (x) = 5x ^ 3 + 9x ^ 2 + 15x + 27`