(x-8)(x-8)

Jasonbradley

2 min read

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Jun 17, 2024

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Expanding (x-8)(x-8)

The expression (x-8)(x-8) is a product of two binomials. To expand this, we can use the FOIL method which stands for:

• First: Multiply the first terms of each binomial.
• Outer: Multiply the outer terms of the binomials.
• Inner: Multiply the inner terms of the binomials.
• Last: Multiply the last terms of each binomial.

Let's apply this method to (x-8)(x-8):

1. First: x * x = x²
2. Outer: x * -8 = -8x
3. Inner: -8 * x = -8x
4. Last: -8 * -8 = 64

Now, combine the terms: x² - 8x - 8x + 64

Finally, simplify by combining the like terms: x² - 16x + 64

Therefore, the expanded form of (x-8)(x-8) is x² - 16x + 64.

Recognizing a Special Case

This expression is a special case known as a perfect square trinomial. This is because it's the result of squaring a binomial. Notice the pattern:

• The first term is the square of the first term of the binomial (x² = x * x)
• The last term is the square of the second term of the binomial (64 = -8 * -8)
• The middle term is twice the product of the two terms of the binomial (-16x = 2 * x * -8)

Understanding this pattern can help you quickly expand similar expressions.