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(x-8)^2 In Standard Form

2 min read Jun 17, 2024
(x-8)^2 In Standard Form

Expanding (x - 8)^2 to Standard Form

The expression (x - 8)^2 represents a squared binomial, which can be rewritten in standard form (ax² + bx + c) by using the distributive property or the FOIL method.

Using the Distributive Property

The distributive property states that a(b + c) = ab + ac. We can apply this to expand (x - 8)^2:

  1. Rewrite the expression: (x - 8)^2 = (x - 8)(x - 8)
  2. Distribute the first term: x(x - 8) - 8(x - 8)
  3. Simplify: x² - 8x - 8x + 64
  4. Combine like terms: x² - 16x + 64

Therefore, (x - 8)^2 expanded in standard form is x² - 16x + 64.

Using the FOIL Method

FOIL stands for First, Outer, Inner, Last, and it's a mnemonic device for remembering how to multiply binomials. We can apply it to expand (x - 8)^2:

  1. Multiply the First terms: x * x = x²
  2. Multiply the Outer terms: x * -8 = -8x
  3. Multiply the Inner terms: -8 * x = -8x
  4. Multiply the Last terms: -8 * -8 = 64
  5. Combine like terms: x² - 8x - 8x + 64 = x² - 16x + 64

Again, we arrive at the same result: x² - 16x + 64.

Conclusion

Both methods demonstrate how to expand (x - 8)^2 into its standard form, x² - 16x + 64. This expansion is crucial for various algebraic operations, such as solving quadratic equations, factoring expressions, and graphing parabolas.

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