Welcome to Westonci.ca, your ultimate destination for finding answers to a wide range of questions from experts. Connect with a community of experts ready to help you find accurate solutions to your questions quickly and efficiently. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
Let's solve the expression step by step in detail. We need to subtract the polynomial [tex]\( \left(d^3 + 6d + 9\right) \)[/tex] from the polynomial [tex]\( \left(d^2 + 6d + 9\right) \)[/tex].
We start by writing down both polynomials:
1. [tex]\( d^2 + 6d + 9 \)[/tex]
2. [tex]\( d^3 + 6d + 9 \)[/tex]
Now perform the subtraction:
[tex]\[ (d^2 + 6d + 9) - (d^3 + 6d + 9) \][/tex]
Distribute the subtraction across each term in the second polynomial:
[tex]\[ d^2 + 6d + 9 - d^3 - 6d - 9 \][/tex]
Next, combine like terms. We will group the terms with the same degree:
1. Combine [tex]\( d^2 \)[/tex] terms: [tex]\( d^2 \)[/tex]
2. Combine [tex]\( 6d \)[/tex] terms: [tex]\( 6d - 6d = 0 \)[/tex]
3. Combine constants: [tex]\( 9 - 9 = 0 \)[/tex]
4. Lastly, don't forget the [tex]\( -d^3 \)[/tex] term.
Resulting in:
[tex]\[ d^2 - d^3 + 0 + 0 \][/tex]
Simplified, it becomes:
[tex]\[ d^2 - d^3 \][/tex]
To write the polynomial in standard form, arrange the terms in order of descending powers of [tex]\( d \)[/tex]:
[tex]\[ -d^3 + d^2 \][/tex]
This matches our target result. Therefore, the polynomial in its simplified standard form is:
[tex]\[ \boxed{-d^3 + d^2} \][/tex]
We start by writing down both polynomials:
1. [tex]\( d^2 + 6d + 9 \)[/tex]
2. [tex]\( d^3 + 6d + 9 \)[/tex]
Now perform the subtraction:
[tex]\[ (d^2 + 6d + 9) - (d^3 + 6d + 9) \][/tex]
Distribute the subtraction across each term in the second polynomial:
[tex]\[ d^2 + 6d + 9 - d^3 - 6d - 9 \][/tex]
Next, combine like terms. We will group the terms with the same degree:
1. Combine [tex]\( d^2 \)[/tex] terms: [tex]\( d^2 \)[/tex]
2. Combine [tex]\( 6d \)[/tex] terms: [tex]\( 6d - 6d = 0 \)[/tex]
3. Combine constants: [tex]\( 9 - 9 = 0 \)[/tex]
4. Lastly, don't forget the [tex]\( -d^3 \)[/tex] term.
Resulting in:
[tex]\[ d^2 - d^3 + 0 + 0 \][/tex]
Simplified, it becomes:
[tex]\[ d^2 - d^3 \][/tex]
To write the polynomial in standard form, arrange the terms in order of descending powers of [tex]\( d \)[/tex]:
[tex]\[ -d^3 + d^2 \][/tex]
This matches our target result. Therefore, the polynomial in its simplified standard form is:
[tex]\[ \boxed{-d^3 + d^2} \][/tex]
We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.