Answer :
The given expression is [tex]\(2x^6 + 9x^3y^2 + 4y^2\)[/tex]. Let's break it down and understand it term by term:
1. First term: [tex]\(2x^6\)[/tex]
- This term consists of a coefficient [tex]\(2\)[/tex] and a variable [tex]\(x\)[/tex] raised to the power of [tex]\(6\)[/tex].
- It represents a polynomial term of degree 6 in terms of [tex]\(x\)[/tex].
2. Second term: [tex]\(9x^3y^2\)[/tex]
- This term has a coefficient [tex]\(9\)[/tex] and a variable [tex]\(x\)[/tex] raised to the power of [tex]\(3\)[/tex], multiplied by another variable [tex]\(y\)[/tex] raised to the power of [tex]\(2\)[/tex].
- This is a mixed term involving both [tex]\(x\)[/tex] and [tex]\(y\)[/tex].
3. Third term: [tex]\(4y^2\)[/tex]
- This term has a coefficient [tex]\(4\)[/tex] and a variable [tex]\(y\)[/tex] raised to the power of [tex]\(2\)[/tex].
- It represents a polynomial term of degree 2 in terms of [tex]\(y\)[/tex].
The expression as a whole is a polynomial in two variables [tex]\(x\)[/tex] and [tex]\(y\)[/tex], and it does not require any further simplification unless specific instructions are given, such as to factor or evaluate for particular values of [tex]\(x\)[/tex] and [tex]\(y\)[/tex].
Therefore, the expression [tex]\(2x^6 + 9x^3y^2 + 4y^2\)[/tex] is presented in its simplest form by listing out the polynomial terms with their respective coefficients and exponents.
1. First term: [tex]\(2x^6\)[/tex]
- This term consists of a coefficient [tex]\(2\)[/tex] and a variable [tex]\(x\)[/tex] raised to the power of [tex]\(6\)[/tex].
- It represents a polynomial term of degree 6 in terms of [tex]\(x\)[/tex].
2. Second term: [tex]\(9x^3y^2\)[/tex]
- This term has a coefficient [tex]\(9\)[/tex] and a variable [tex]\(x\)[/tex] raised to the power of [tex]\(3\)[/tex], multiplied by another variable [tex]\(y\)[/tex] raised to the power of [tex]\(2\)[/tex].
- This is a mixed term involving both [tex]\(x\)[/tex] and [tex]\(y\)[/tex].
3. Third term: [tex]\(4y^2\)[/tex]
- This term has a coefficient [tex]\(4\)[/tex] and a variable [tex]\(y\)[/tex] raised to the power of [tex]\(2\)[/tex].
- It represents a polynomial term of degree 2 in terms of [tex]\(y\)[/tex].
The expression as a whole is a polynomial in two variables [tex]\(x\)[/tex] and [tex]\(y\)[/tex], and it does not require any further simplification unless specific instructions are given, such as to factor or evaluate for particular values of [tex]\(x\)[/tex] and [tex]\(y\)[/tex].
Therefore, the expression [tex]\(2x^6 + 9x^3y^2 + 4y^2\)[/tex] is presented in its simplest form by listing out the polynomial terms with their respective coefficients and exponents.
