(3a-2)(3a+2)+(a-8)(a+8)

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression: (3a-2)(3a+2)+(a-8)(a+8)

This expression involves the product of two binomials. To simplify it, we can use the following algebraic identities:

• Difference of Squares: (x-y)(x+y) = x² - y²

Let's break down the simplification:

Step 1: Apply the difference of squares identity to both terms:

• (3a-2)(3a+2) = (3a)² - (2)² = 9a² - 4
• (a-8)(a+8) = (a)² - (8)² = a² - 64

Step 2: Substitute the simplified terms back into the original expression:

(3a-2)(3a+2)+(a-8)(a+8) = (9a² - 4) + (a² - 64)

Step 3: Combine like terms:

9a² - 4 + a² - 64 = 10a² - 68

Therefore, the simplified form of the expression (3a-2)(3a+2)+(a-8)(a+8) is 10a² - 68.