To rewrite the given polynomials in standard form, we follow these steps:
1. Identify all the terms of the polynomial.
2. Arrange the terms in descending order of the power of the variable.
Let's go through each polynomial step by step:
### Part i: \(4y - 4y^3 + 3 - y^4\)
1. Identify the terms: \(4y\), \(-4y^3\), \(3\), and \(-y^4\).
2. Arrange the terms in descending order of the power of \(y\):
- The term with \(y^4\) comes first.
- The term with \(y^3\) comes next.
- The term with \(y\) follows that.
- The constant term comes last.
So, the polynomial in standard form is:
[tex]\[ -y^4 - 4y^3 + 4y + 3 \][/tex]
### Part ii: \(5m^3 - 6m + 7 - 2m^2\)
1. Identify the terms: \(5m^3\), \(-6m\), \(7\), and \(-2m^2\).
2. Arrange the terms in descending order of the power of \(m\):
- The term with \(m^3\) comes first.
- The term with \(m^2\) comes next.
- The term with \(m\) comes after that.
- The constant term comes last.
So, the polynomial in standard form is:
[tex]\[ 5m^3 - 2m^2 - 6m + 7 \][/tex]
### Conclusion
The standard form of the given polynomials are:
i. \( -y^4 - 4y^3 + 4y + 3 \)
ii. [tex]\( 5m^3 - 2m^2 - 6m + 7 \)[/tex]
