\begin{tabular}{l} Directions: Write the following polynomials in standard form. \\ \begin{tabular}{l|l} 7. \( y^{2}+3 y^{4}-7 y+2 y^{3}-4 \) & 8. \( 9 x^{4}-2 x^{2}+7 x-8 x^{3}+x^{5}-4 \) \\ \\ \( \begin{array}{l}3 y^{4}+2 y^{3}+y^{2}-7 y-4\end{array} \) & \( 7 x^{5}-4 \)\end{tabular} \\ \hline 9. \( -2 b^{2}+5 a b+7 a^{2} \)\end{tabular}

To write the given polynomials in standard form, we need to arrange the terms in descending order of their degrees. Let's go through each polynomial step by step. ### Problem 7: \( y^{2}+3 y^{4}-7 y+2 y^{3}-4 \) 1. Identify the degrees of each term: - \( 3y^4 \) (degree 4) - \( 2y^3 \) (degree 3) - \( y^2 \) (degree 2) - \( -7y \) (degree 1) - \( -4 \) (degree 0) 2. Arrange the terms in descending order: - \( 3y^4 + 2y^3 + y^2 - 7y - 4 \) Thus, the polynomial in standard form is: \[ 3y^4 + 2y^3 + y^2 - 7y - 4 \] ### Problem 8: \( 9 x^{4}-2 x^{2}+7 x-8 x^{3}+x^{5}-4 \) 1. Identify the degrees of each term: - \( x^5 \) (degree 5) - \( -8x^3 \) (degree 3) - \( 9x^4 \) (degree 4) - \( -2x^2 \) (degree 2) - \( 7x \) (degree 1) - \( -4 \) (degree 0) 2. Arrange the terms in descending order: - \( x^5 - 8x^3 + 9x^4 - 2x^2 + 7x - 4 \) Thus, the polynomial in standard form is: \[ x^5 - 8x^3 + 9x^4 - 2x^2 + 7x - 4 \] ### Problem 9: \( -2 b^{2}+5 a b+7 a^{2} \) 1. Identify the degrees of each term: - \( 7a^2 \) (degree 2) - \( 5ab \) (degree 2) - \( -2b^2 \) (degree 2) 2. Since all terms are of degree 2, we can arrange them based on the variables: - \( 7a^2 + 5ab - 2b^2 \) Thus, the polynomial in standard form is: \[ 7a^2 + 5ab - 2b^2 \] ### Summary of Results 1. \( 3y^4 + 2y^3 + y^2 - 7y - 4 \) 2. \( x^5 - 8x^3 + 9x^4 - 2x^2 + 7x - 4 \) 3. \( 7a^2 + 5ab - 2b^2 \)