(x-4)-answer.jpeg "(x-4)(x-4) Answer")
Simplifying (x-4)(x-4)
The expression (x-4)(x-4) is a product of two binomials. To simplify it, we can use the distributive property (also known as FOIL - First, Outer, Inner, Last) or recognize it as a special case of squaring a binomial.
Using the Distributive Property
- Multiply the First terms: x * x = x²
- Multiply the Outer terms: x * -4 = -4x
- Multiply the Inner terms: -4 * x = -4x
- Multiply the Last terms: -4 * -4 = 16
Now, combine the like terms:
x² - 4x - 4x + 16 = x² - 8x + 16
Squaring a Binomial
Recognizing that (x-4)(x-4) is simply (x-4)², we can use the following formula:
(a - b)² = a² - 2ab + b²
In our case, a = x and b = 4. Applying the formula:
(x - 4)² = x² - 2(x)(4) + 4² = x² - 8x + 16
Conclusion
Both methods lead to the same simplified expression: x² - 8x + 16. This is the expanded form of the product (x-4)(x-4).