(-5x+7)^2

2 min read Jun 16, 2024
(-5x+7)^2

Expanding the Square of a Binomial: (-5x + 7)^2

The expression (-5x + 7)^2 represents the square of a binomial. To expand this expression, we can apply the FOIL method or the square of a binomial pattern.

Using the FOIL Method

FOIL stands for First, Outer, Inner, Last. This method helps us to multiply two binomials systematically.

  1. First: Multiply the first terms of each binomial: (-5x) * (-5x) = 25x²
  2. Outer: Multiply the outer terms: (-5x) * 7 = -35x
  3. Inner: Multiply the inner terms: 7 * (-5x) = -35x
  4. Last: Multiply the last terms: 7 * 7 = 49

Now, we add all the products together: 25x² - 35x - 35x + 49

Combining like terms, we get the final expanded form: 25x² - 70x + 49

Using the Square of a Binomial Pattern

The square of a binomial pattern is: (a + b)² = a² + 2ab + b²

In our case, a = -5x and b = 7. Substituting these values into the pattern:

(-5x)² + 2(-5x)(7) + 7²

Simplifying: 25x² - 70x + 49

Both methods result in the same expanded form: 25x² - 70x + 49

Therefore, the expanded form of (-5x + 7)² is 25x² - 70x + 49.

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