2.jpeg "(2x+7y)2")
Expanding (2x + 7y)²
In mathematics, expanding an expression means writing it in a simpler form without parentheses. When dealing with squares of binomials like (2x + 7y)², we can use the FOIL method or the square of a binomial formula.
Using the FOIL Method
FOIL stands for First, Outer, Inner, Last. This method helps us multiply two binomials by systematically multiplying each term in the first binomial with each term in the second.
- First: Multiply the first terms of each binomial: (2x) * (2x) = 4x²
- Outer: Multiply the outer terms of the binomials: (2x) * (7y) = 14xy
- Inner: Multiply the inner terms of the binomials: (7y) * (2x) = 14xy
- Last: Multiply the last terms of each binomial: (7y) * (7y) = 49y²
Finally, combine the results: 4x² + 14xy + 14xy + 49y² = 4x² + 28xy + 49y²
Using the Square of a Binomial Formula
The square of a binomial formula states: (a + b)² = a² + 2ab + b²
- Identify 'a' and 'b': In this case, a = 2x and b = 7y.
- Apply the formula: (2x)² + 2(2x)(7y) + (7y)²
- Simplify: 4x² + 28xy + 49y²
Conclusion
Both methods arrive at the same answer: (2x + 7y)² = 4x² + 28xy + 49y². The FOIL method is more intuitive, while the formula provides a direct approach. Choose whichever method you find easier to understand and apply.