(a-8)^2-4a

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression (a-8)^2 - 4a

This article will guide you through the process of simplifying the expression (a-8)^2 - 4a. We'll use the principles of algebraic manipulation to achieve a more concise and understandable form.

Understanding the Expression

The expression consists of two main parts:

• (a-8)^2: This represents the square of the binomial (a-8).
• -4a: This is a simple term with a coefficient of -4 and the variable 'a'.

Simplifying the Expression

1. Expand the Square: We start by expanding the square of the binomial. Remember that squaring a binomial means multiplying it by itself:

   (a-8)^2 = (a-8)(a-8)

   Using the distributive property (or FOIL method), we get:

   (a-8)^2 = a^2 - 8a - 8a + 64 = a^2 - 16a + 64

2. Combine Terms: Now we can substitute the expanded form back into the original expression:

   (a-8)^2 - 4a = a^2 - 16a + 64 - 4a

3. Simplify: Combine the 'a' terms:

   a^2 - 16a + 64 - 4a = a^2 - 20a + 64

Final Result

Therefore, the simplified form of the expression (a-8)^2 - 4a is a^2 - 20a + 64.

This simplified form makes it easier to analyze the expression, perform further operations, or solve equations involving it.