2.jpeg "(b-7)2")
Understanding (b - 7)<sup>2</sup>
(b - 7)<sup>2</sup> is a mathematical expression that represents the square of the difference between a variable 'b' and the constant 7. Let's break down what this means and how to expand it:
What Does Squaring Mean?
Squaring a number means multiplying it by itself. So, (b - 7)<sup>2</sup> is equivalent to:
(b - 7) * (b - 7)
Expanding the Expression
To expand the expression, we need to use the FOIL method (First, Outer, Inner, Last) for multiplying binomials:
- First: Multiply the first terms of each binomial: b * b = b<sup>2</sup>
- Outer: Multiply the outer terms of each binomial: b * -7 = -7b
- Inner: Multiply the inner terms of each binomial: -7 * b = -7b
- Last: Multiply the last terms of each binomial: -7 * -7 = 49
Now, combine the terms:
b<sup>2</sup> - 7b - 7b + 49
Finally, simplify by combining the like terms:
b<sup>2</sup> - 14b + 49
Conclusion
Therefore, the expanded form of (b - 7)<sup>2</sup> is b<sup>2</sup> - 14b + 49. This expression can be useful in various mathematical contexts, including solving equations, simplifying expressions, and understanding the relationship between variables.