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(2x-7)^2 Simplify

2 min read Jun 16, 2024
(2x-7)^2 Simplify

Simplifying (2x - 7)^2

The expression (2x - 7)^2 represents the square of the binomial (2x - 7). To 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. This method helps to multiply two binomials.

  1. First: Multiply the first terms of each binomial: (2x) * (2x) = 4x²
  2. Outer: Multiply the outer terms of the binomials: (2x) * (-7) = -14x
  3. Inner: Multiply the inner terms of the binomials: (-7) * (2x) = -14x
  4. Last: Multiply the last terms of each binomial: (-7) * (-7) = 49

Now, add all the terms together: 4x² - 14x - 14x + 49

Finally, combine the like terms: 4x² - 28x + 49

Using the Square of a Binomial Formula

The square of a binomial formula states: (a - b)² = a² - 2ab + b²

In our case, a = 2x and b = 7. Applying the formula:

(2x - 7)² = (2x)² - 2(2x)(7) + (7)²

Simplifying: 4x² - 28x + 49

Therefore, the simplified form of (2x - 7)² is 4x² - 28x + 49.

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