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(7x+2)^2 Simplify

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

Simplifying (7x + 2)^2

The expression (7x + 2)^2 represents the square of a binomial. To simplify this, we need to expand the expression using the FOIL method or the square of a binomial pattern.

Expanding with FOIL

FOIL stands for First, Outer, Inner, Last. This method helps us multiply two binomials by considering each term of the first binomial with each term of the second binomial.

  1. First: (7x) * (7x) = 49x²
  2. Outer: (7x) * (2) = 14x
  3. Inner: (2) * (7x) = 14x
  4. Last: (2) * (2) = 4

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

Finally, combine like terms to get the simplified expression: 49x² + 28x + 4

Using the Square of a Binomial Pattern

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

In our case, a = 7x and b = 2. Applying the pattern, we get:

(7x + 2)² = (7x)² + 2(7x)(2) + (2)²

Simplifying the expression: 49x² + 28x + 4

Conclusion

Therefore, the simplified form of (7x + 2)² is 49x² + 28x + 4. Both the FOIL method and the square of a binomial pattern lead to the same result. Choose the method that feels more comfortable for you.

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