QuestionFind $(c \cdot d)(x)$ for $c(x)=4x-2$ and $d(x)=x^2+5x$ .

Studdy Solution

STEP 1

Assumptions1. We have two functions, $c(x)=4x-$ and $d(x)=x^{}+5x$ . . We need to find the product of these two functions, denoted as $(c \cdot d)(x)$ .

STEP 2

The product of two functions $c(x)$ and $d(x)$ is defined as $(c \cdot d)(x) = c(x) \cdot d(x)$ .

STEP 3

Substitute the given functions into the product.
$(c \cdot d)(x) = (x-2) \cdot (x^{2}+5x)$

STEP 4

To multiply these two expressions, we use the distributive property of multiplication over addition, which states that $a \cdot (b + c) = a \cdot b + a \cdot c$ .
(c \cdot d)(x) =4x \cdot x^{2} +4x \cdotx -2 \cdot x^{2} -2 \cdotx

STEP 5

implify the above expression.
$(c \cdot d)(x) =4x^{3} +20x^{2} -2x^{2} -10x$

STEP 6

Combine like terms.
$(c \cdot d)(x) =4x^{3} + (20x^{2} -2x^{2}) -10x$

STEP 7

Calculate the final expression.
$(c \cdot d)(x) =4x^{3} +18x^{2} -10x$ So, $(c \cdot d)(x) =4x^{3} +18x^{2} -10x$ .

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms