%5E2.jpeg "(b+7)^2")
Expanding (b + 7)²
The expression (b + 7)² represents the square of the binomial (b + 7). To expand this expression, we can use the FOIL method or the square of a binomial pattern.
Using the FOIL Method
FOIL stands for First, Outer, Inner, Last. This method helps us multiply each term in the first binomial by each term in the second binomial:
- First: Multiply the first terms of each binomial: b * b = b²
- Outer: Multiply the outer terms of the binomials: b * 7 = 7b
- Inner: Multiply the inner terms of the binomials: 7 * b = 7b
- Last: Multiply the last terms of each binomial: 7 * 7 = 49
Now, combine the results:
b² + 7b + 7b + 49
Finally, simplify by combining the like terms:
b² + 14b + 49
Using the Square of a Binomial Pattern
The square of a binomial pattern is: (a + b)² = a² + 2ab + b²
Applying this to our expression:
a = b b = 7
Substituting these values into the pattern:
b² + 2(b)(7) + 7²
Simplifying:
b² + 14b + 49
Conclusion
Both methods lead to the same expanded expression: b² + 14b + 49. This is the simplified form of (b + 7)².