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(y+3)^2 Simplify

2 min read Jun 17, 2024
(y+3)^2 Simplify

Simplifying (y+3)^2

The expression (y+3)^2 represents the square of the binomial (y+3). To simplify this, we can apply the FOIL method or the square of a binomial pattern.

FOIL Method

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

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

Now, we add all the terms together: y^2 + 3y + 3y + 9

Finally, we combine the like terms: y^2 + 6y + 9

Therefore, (y+3)^2 simplified is y^2 + 6y + 9

Square of a Binomial Pattern

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

Applying this pattern to our expression:

  • a = y
  • b = 3

Substituting these values in the pattern: y^2 + 2(y)(3) + 3^2

Simplifying this expression gives us: y^2 + 6y + 9

This method provides a quicker way to simplify the expression.

Conclusion

Both the FOIL method and the square of a binomial pattern lead to the same simplified expression: y^2 + 6y + 9. Choose the method you find easiest and most comfortable to apply.

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