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(9x+1)^2

2 min read Jun 16, 2024
(9x+1)^2

Expanding (9x+1)^2

The expression (9x+1)^2 represents the square of the binomial (9x+1). To expand this expression, we can use the FOIL method or the square of a binomial formula.

FOIL Method

FOIL stands for First, Outer, Inner, Last. This method involves multiplying each term of the first binomial by each term of the second binomial.

  1. First: Multiply the first terms of each binomial: 9x * 9x = 81x^2
  2. Outer: Multiply the outer terms of the binomials: 9x * 1 = 9x
  3. Inner: Multiply the inner terms of the binomials: 1 * 9x = 9x
  4. Last: Multiply the last terms of each binomial: 1 * 1 = 1

Now we add all the terms together: 81x^2 + 9x + 9x + 1

Finally, we combine the like terms: 81x^2 + 18x + 1

Square of a Binomial Formula

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

Applying this to our problem:

  • a = 9x
  • b = 1

Substituting these values into the formula:

(9x + 1)^2 = (9x)^2 + 2(9x)(1) + (1)^2

Simplifying:

(9x + 1)^2 = 81x^2 + 18x + 1

Conclusion

Both the FOIL method and the square of a binomial formula lead to the same expanded expression: 81x^2 + 18x + 1.

This expanded form is essential for solving equations, simplifying expressions, and performing other algebraic operations involving (9x+1)^2.

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