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When we talk about simplifying expressions in algebra, we refer to the process of reducing expressions to their most basic form. - **Combine Like Terms**: We look for terms that have the same variables raised to the same powers. These can be combined by adding or subtracting their coefficients. - **Perform Operations**: Carry out basic arithmetic operations (addition, subtraction, multiplication, and division). The goal is to make expressions as straightforward as possible. In the exercise given, we dealt with multiplication, reducing it by considering exponents and simplifying the coefficients of like terms, resulting in a much cleaner and more straightforward expression.

The distributive property is a fundamental principle in algebra that makes it possible to multiply a single term by a sum or a difference easily. - **How it Works**: When you distribute, multiply the term outside the brackets by each term inside. For example, \((a(b + c) = ab + ac\)). Distribution can also apply to two terms as seen in the problem \((3x^2y)(-4xy^2)\),where each part of the first term is multiplied with each part of the second term individually: - Multiply the coefficients: \(3 imes -4 = -12\) - Multiply the variables by adding exponents placed on the same variables together.This property simplifies expressions and solves complex problems efficiently by breaking them into smaller parts.

Exponents help indicate how many times a number is to be multiplied by itself. - **Basic Rule**: When multiplying two powers with the same base, you add their exponents: \(x^m \times x^n = x^{m+n}\).For the given exercise, this rule allows you to combine the powers of variables: - For \(x\): \(x^2 \times x = x^{2+1} = x^3\) - For \(y\): \(y imes y^2 = y^{1+2} = y^3\).Algebra with exponents is centered around knowing and applying these rules effectively. It makes handling larger expressions and variables more manageable and systematic.