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(7a-1)^2

2 min read Jun 16, 2024
(7a-1)^2

Expanding (7a-1)^2

The expression (7a-1)^2 represents the square of the binomial (7a-1). To expand this expression, we can use the FOIL method or the square of a binomial formula.

Expanding using FOIL

FOIL stands for First, Outer, Inner, Last. It's a method for multiplying two binomials. Here's how it applies to our expression:

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

Now, add all the terms together: 49a^2 - 7a - 7a + 1

Finally, combine the like terms: 49a^2 - 14a + 1

Expanding using the square of a binomial formula

The square of a binomial formula states: (a + b)^2 = a^2 + 2ab + b^2

Applying this to our expression:

  1. Identify 'a' and 'b': a = 7a and b = -1
  2. Substitute the values into the formula: (7a)^2 + 2 (7a) (-1) + (-1)^2
  3. Simplify: 49a^2 - 14a + 1

Conclusion

Both methods lead to the same expanded form of (7a-1)^2, which is 49a^2 - 14a + 1. Remember, the FOIL method is helpful for expanding any two binomials, while the square of a binomial formula is specifically useful for squaring binomials.

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