(2x+3)2 Answer

2 min read Jun 16, 2024
(2x+3)2 Answer

Expanding the Expression (2x + 3)²

In mathematics, expanding an expression means rewriting it in a simpler form without any parentheses. The expression (2x + 3)² involves squaring a binomial, which can be done using the FOIL method or the square of a binomial formula.

Using FOIL Method

FOIL stands for First, Outer, Inner, Last, and it helps to multiply each term in the first binomial by each term in the second binomial.

  1. First: Multiply the first terms of each binomial: (2x) * (2x) = 4x²
  2. Outer: Multiply the outer terms of the binomials: (2x) * (3) = 6x
  3. Inner: Multiply the inner terms of the binomials: (3) * (2x) = 6x
  4. Last: Multiply the last terms of each binomial: (3) * (3) = 9

Adding these products together gives us: 4x² + 6x + 6x + 9

Combining like terms, we get the final expanded expression: 4x² + 12x + 9

Using Square of a Binomial Formula

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

In this case, a = 2x and b = 3. Applying the formula, we get:

(2x + 3)² = (2x)² + 2(2x)(3) + (3)²

Simplifying, we arrive at the same result: 4x² + 12x + 9

Conclusion

Therefore, the expanded form of (2x + 3)² is 4x² + 12x + 9. Both the FOIL method and the square of a binomial formula can be used to achieve the same result. Choose whichever method you find easier to apply.

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