Question

product and quotient functions
m(x) = x² + 4x
n(x) = x
(mn)(x) =
x²+4x(x)
(x²+4x)(x) ✔️
complete
which is equal to:
x³+4x²
5x²
4x⁴
done ✔️

Explanation:

Step1: Recall the product of functions

The product of two functions \((mn)(x)\) is defined as \(m(x) \cdot n(x)\). We know \(m(x)=x^{2}+4x\) and \(n(x)=x\), so \((mn)(x)=(x^{2}+4x)(x)\).

Step2: Distribute the \(x\)

Using the distributive property (also known as the distributive law of multiplication over addition), we multiply each term inside the parentheses by \(x\).
For the first term: \(x^{2} \cdot x = x^{2 + 1}=x^{3}\) (using the rule of exponents \(a^{m}\cdot a^{n}=a^{m + n}\)).
For the second term: \(4x\cdot x = 4x^{1+1}=4x^{2}\) (again using the exponent rule).
Then we add the two results together: \(x^{3}+4x^{2}\).

Answer:

\(x^{3}+4x^{2}\) (corresponding to the first option among the "Which is equal to:" choices)