(x-5).jpeg "(x+6)(x-5)")
Expanding (x + 6)(x - 5)
This expression represents the product of two binomials: (x + 6) and (x - 5). To expand it, we can use the FOIL method:
First: Multiply the first terms of each binomial.
- x * x = x²
Outer: Multiply the outer terms of the binomials.
- x * -5 = -5x
Inner: Multiply the inner terms of the binomials.
- 6 * x = 6x
Last: Multiply the last terms of each binomial.
- 6 * -5 = -30
Now, add all the terms together:
x² - 5x + 6x - 30
Finally, combine the like terms:
x² + x - 30
Therefore, the expanded form of (x + 6)(x - 5) is x² + x - 30.
Understanding the Process
The FOIL method is a helpful mnemonic device to remember the steps involved in multiplying two binomials. It ensures that you multiply each term in the first binomial by each term in the second binomial.
This expansion is important because it allows us to manipulate and solve various algebraic equations and expressions. For example, we can use this expansion to:
- Factor quadratic expressions: We can reverse the process and factor the expression x² + x - 30 back into (x + 6)(x - 5).
- Solve quadratic equations: By setting the expression equal to zero (x² + x - 30 = 0), we can find the values of x that make the equation true.
Understanding the expansion of binomials like (x + 6)(x - 5) is a fundamental skill in algebra, allowing you to tackle more complex mathematical concepts.