Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Subtract
-3c^(2)+12 cd-4d^(2) from
4c^(2)+3cd+2d^(2). Your answer should be a polynomial in standard form.

Subtract $-3 c^{2}+12 c d-4 d^{2}$ from $4 c^{2}+3 c d+2 d^{2}$ . Your answer should be a polynomial in standard form.

View step-by-step help

View step-by-step help

Composition of linear functions: find an equation

Full solution

Q. Subtract

-3 c^{2}+12 c d-4 d^{2}

from

4 c^{2}+3 c d+2 d^{2}

. Your answer should be a polynomial in standard form.

Write Polynomials to Subtract: Write down the polynomials that need to be subtracted. $\newline$ We have the first polynomial $4c^2 + 3cd + 2d^2$ and we need to subtract the second polynomial $-3c^2 + 12cd - 4d^2$ from it.
Change Signs of Second Polynomial: Change the signs of the second polynomial before subtracting. $\newline$ To subtract the second polynomial, we need to change the signs of all its terms and then add it to the first polynomial. $\newline$ So, $-3c^2$ becomes $+3c^2$ , $12cd$ becomes $-12cd$ , and $-4d^2$ becomes $+4d^2$ .
Add Corresponding Terms: Add the corresponding terms of the resulting polynomials. $\newline$ Now, we combine like terms from the first polynomial and the sign-changed second polynomial. $\newline$ $(4c^2 + 3cd + 2d^2) + (3c^2 - 12cd + 4d^2)$
Perform Addition: Perform the addition. $\newline$ Add the $c^2$ terms: $4c^2 + 3c^2 = 7c^2$ $\newline$ Add the $cd$ terms: $3cd - 12cd = -9cd$ $\newline$ Add the $d^2$ terms: $2d^2 + 4d^2 = 6d^2$
Write Final Answer: Write the final answer in standard form. $\newline$ The resulting polynomial in standard form is: $\newline$ $7c^2 - 9cd + 6d^2$

More problems from Composition of linear functions: find an equation

Question

Find the inverse of the function.

y = x + 3

Write your answer in the form

ax + b

. Simplify any fractions.

y =

Posted 2 months ago

Question

(r \circ s)(x)

\newline

3

\newline

2

5

\newline

Write your answer as a polynomial in simplest form.

\newline

(r \circ s)(x) =

Posted 1 month ago

Question

(f + g)(x)

\newline

f(x) = -3x

\newline

g(x) = 3x + 1

\newline

\newline

Write your answer as a polynomial or a rational function in simplest form.

\newline

\underline{\hspace{3cm}}

\newline

Posted 1 month ago

Question

(f * g)(x)

\newline

f(x) = -x + 4

\newline

g(x) = 4x

\newline

\newline

Write your answer as a polynomial or a rational function in simplest form.

\newline

\underline{\hspace{3em}}

\newline

Posted 1 month ago

Question

What is the domain of

\left(\frac{f}{g}\right)(x)

\newline

f(x) = 2x

\newline

g(x) = -5x + 3

\newline

\newline

[\text{A]All real numbers}

\newline

[\text{B]All real numbers except } \frac{3}{5}

\newline

[\text{C]All real numbers except } -\frac{3}{5}

\newline

[\text{D]All real numbers except } \frac{5}{3}

Posted 2 months ago

Question

Find the inverse of the function.

\newline

-3x

\newline

Write your answer in the form

ax + b

. Simplify any fractions.

\newline

Posted 1 month ago

Question

(f \circ g)(0)

\newline

f(x) = 6x

\newline

g(x) = x^2 + 4x

\newline

(f \circ g)(0) =

Posted 1 month ago

Question

(f \circ g)(x)

\newline

f(x) = x^2 + 5

\newline

g(x) = 4x

\newline

Write your answer as a polynomial in simplest form.

\newline

(f \circ g)(x) =

Posted 1 month ago

Question

f(x)

the inverse function of

g(x)

\newline

f(x) = x

\newline

g(x) = -4x

\newline

\newline

\text{[yes]}

\newline

\text{[no]}

Posted 1 month ago

Question

(f * g)(x)

f(x) = 3x^2 + 9x

g(x) = 3x

Write your answer as a polynomial or a rational function in simplest form. ______

Posted 2 months ago