91Ó°ÊÓ

Polynomial multiplication involves expanding expressions where polynomials are multiplied together.
In the given exercise, we have a single term \( -6 \) multiplied by the polynomial \( -5y^2 - 3y + 4 \).
To perform this multiplication, use the distributive property.
Distribute \( -6 \) to each term inside the polynomial.
This ensures that all components of the polynomial are scaled proportionately.
For example, when multiplying \( -6(-5y^2) \), we multiply the coefficients (numbers in front of the variables) together while maintaining the variable part unchanged.
Hence, \( -6 \times -5 = 30 \), and the term \( y^2 \) remains \( y^2 \), resulting in \( 30y^2 \).
Repeat this process for all terms inside the parentheses to achieve the expanded polynomial.

Algebraic expressions are combinations of variables, numbers, and operations.
Each term in an algebraic expression can include a variable (like \( y \)), a coefficient (a number), and an exponent (power).
In our exercise, the expression \( -5y^2 - 3y + 4 \) consists of three terms:

• \(-5y^2 \): a term with a variable squared,
• \(-3y \): a term with a first-degree variable,
• \( 4 \): a constant term.

Distributive property plays a crucial role in simplifying these expressions, especially when factoring or expanding.
Understanding each term's components helps in breaking down and correctly applying operations to it.

Mathematical operations refer to the foundational processes in arithmetic: addition, subtraction, multiplication, and division.
In our exercise, multiplication and addition are primarily involved.
The key steps are:

• Multiplication: Applying distributive property requires multiplying the external term \(-6 \) with each internal term (like \(-5y^2 , -3y, \) and \(4 \)) individually.
  It’s important to handle the negative signs correctly to avoid mistakes.
  
• Addition/Subtraction: After multiplying, combine the resulting terms.
  Remember to keep the signs (positive or negative) intact for each term during addition.
  

By following these operations methodically, simplifying polynomial expressions becomes straightforward and manageable.