(-5cd-4)(2cd2)2

Jasonbradley

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Jun 17, 2024

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Simplifying the Expression (-5cd-4)(2cd^2)^2

This article will guide you through simplifying the expression (-5cd-4)(2cd^2)^2.

Understanding the Expression

The expression consists of two parts:

• (-5cd-4): This is a binomial (an expression with two terms) with variables c and d.
• (2cd^2)^2: This is a monomial (an expression with one term) with variables c and d, raised to the power of 2.

Simplifying the Expression

To simplify the expression, we will follow the order of operations (PEMDAS/BODMAS):

1. Parentheses/Brackets:

   • First, we need to simplify the expression within the parentheses (2cd^2)^2. Applying the power rule of exponents, we square each term inside the parentheses: (2cd^2)^2 = 2^2 * c^2 * (d^2)^2 = 4c^2d^4

2. Multiplication:

   • Now, we have simplified the expression to: (-5cd-4)(4c^2d^4). To multiply these two expressions, we use the distributive property, multiplying each term in the first binomial by the second monomial:

   (-5cd)(4c^2d^4) + (-4)(4c^2d^4)

3. Simplifying Terms:

   • Finally, we multiply the coefficients and combine the variables: -20c^3d^5 - 16c^2d^4

Result

Therefore, the simplified expression of (-5cd-4)(2cd^2)^2 is -20c^3d^5 - 16c^2d^4.