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(4a-7)^2

2 min read Jun 16, 2024
(4a-7)^2

Expanding (4a-7)^2

The expression (4a-7)^2 represents the square of the binomial (4a-7). To expand it, we can use the FOIL method or the square of a binomial formula.

Using the FOIL Method

FOIL stands for First, Outer, Inner, Last. It helps us remember the order in which to multiply the terms of the binomials:

  1. First: Multiply the first terms of each binomial: (4a) * (4a) = 16a²
  2. Outer: Multiply the outer terms of the binomials: (4a) * (-7) = -28a
  3. Inner: Multiply the inner terms of the binomials: (-7) * (4a) = -28a
  4. Last: Multiply the last terms of each binomial: (-7) * (-7) = 49

Now, add all the products: 16a² - 28a - 28a + 49

Combining like terms, we get the final expanded form: 16a² - 56a + 49

Using the Square of a Binomial Formula

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

Applying this formula to our problem:

  1. a = 4a
  2. b = 7

Substitute these values into the formula: (4a)² - 2(4a)(7) + 7²

Simplifying the expression: 16a² - 56a + 49

Therefore, the expanded form of (4a-7)² is 16a² - 56a + 49, regardless of the method used.

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