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(x-4)^2 Expand And Simplify

2 min read Jun 17, 2024
(x-4)^2 Expand And Simplify

Expanding and Simplifying (x - 4)^2

The expression (x - 4)^2 represents the square of the binomial (x - 4). To expand and simplify this expression, we can use the FOIL method or the square of a binomial formula.

Using the FOIL Method

FOIL stands for First, Outer, Inner, Last, and it's a way to multiply two binomials. Let's apply it to our expression:

  1. First: Multiply the first terms of each binomial: x * x = x^2
  2. Outer: Multiply the outer terms: x * -4 = -4x
  3. Inner: Multiply the inner terms: -4 * x = -4x
  4. Last: Multiply the last terms: -4 * -4 = 16

Now, we combine all the terms: x^2 - 4x - 4x + 16

Finally, simplify by combining like terms:

x^2 - 8x + 16

Using the Square of a Binomial Formula

The formula for the square of a binomial is:

(a - b)^2 = a^2 - 2ab + b^2

Applying this formula to (x - 4)^2:

  • a = x
  • b = 4

Substitute the values into the formula:

x^2 - 2(x)(4) + 4^2

Simplify:

x^2 - 8x + 16

Conclusion

Both methods lead to the same simplified expression: x^2 - 8x + 16. This demonstrates that expanding and simplifying algebraic expressions can be done in different ways, but the result is always the same.

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