%5E2.jpeg "(u-7)^2")
Expanding (u-7)^2: A Step-by-Step Guide
The expression (u-7)^2 represents the square of the binomial (u-7). To expand this, we need to apply the distributive property or the FOIL method.
Understanding the Basics
- Binomial: An algebraic expression with two terms, like (u-7).
- Square: Multiplying a number or expression by itself.
- FOIL Method: An acronym for "First, Outer, Inner, Last". It helps multiply binomials systematically.
Expanding using the FOIL Method
- First: Multiply the first terms of each binomial: u * u = u²
- Outer: Multiply the outer terms: u * -7 = -7u
- Inner: Multiply the inner terms: -7 * u = -7u
- Last: Multiply the last terms: -7 * -7 = 49
Now, combine all the terms:
u² - 7u - 7u + 49
Finally, simplify by combining like terms:
u² - 14u + 49
Expanding using the Distributive Property
- Rewrite (u-7)^2 as (u-7)(u-7)
- Distribute the first term of the first binomial across the second binomial: u(u-7) - 7(u-7)
- Distribute further: u² - 7u - 7u + 49
- Combine like terms: u² - 14u + 49
Conclusion
Both methods lead to the same expanded form of (u-7)²: u² - 14u + 49. This expression is now in a simplified form, allowing for further manipulation or analysis in various mathematical contexts.