2.jpeg "(6x+7)2")
Expanding the Expression (6x + 7)²
The expression (6x + 7)² represents the square of a binomial. To expand it, 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 each term in the first binomial with each term in the second binomial:
- First: Multiply the first terms of each binomial: (6x)(6x) = 36x²
- Outer: Multiply the outer terms of the binomials: (6x)(7) = 42x
- Inner: Multiply the inner terms of the binomials: (7)(6x) = 42x
- Last: Multiply the last terms of each binomial: (7)(7) = 49
Now, combine the terms: 36x² + 42x + 42x + 49
Simplify the expression by combining like terms: 36x² + 84x + 49
Using the Square of a Binomial Formula
The square of a binomial formula states: (a + b)² = a² + 2ab + b²
In our case, a = 6x and b = 7. Applying the formula:
(6x + 7)² = (6x)² + 2(6x)(7) + 7²
Simplifying the expression: 36x² + 84x + 49
Conclusion
Both the FOIL method and the square of a binomial formula lead to the same expanded expression: 36x² + 84x + 49.
This expanded form is a quadratic trinomial with a leading coefficient of 36, a linear coefficient of 84, and a constant term of 49.