2-answer.jpeg "(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.
- First: Multiply the first terms of each binomial: (2x) * (2x) = 4x²
- Outer: Multiply the outer terms of the binomials: (2x) * (3) = 6x
- Inner: Multiply the inner terms of the binomials: (3) * (2x) = 6x
- 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.