(x-6)(x+7)

Jasonbradley

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Jun 17, 2024

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Factoring and Expanding: A Look at (x-6)(x+7)

The expression (x-6)(x+7) represents a product of two binomials. Let's delve into its factoring and expansion.

Factoring

Factoring is the process of breaking down an expression into its simpler multiplicative components. In this case, the expression is already factored as a product of two binomials: (x-6) and (x+7).

Expanding

Expanding the expression means multiplying the two binomials together to obtain a polynomial. We can use the distributive property, also known as FOIL (First, Outer, Inner, Last) to achieve this.

1. First: Multiply the first terms of each binomial: x * x = x²
2. Outer: Multiply the outer terms of the binomials: x * 7 = 7x
3. Inner: Multiply the inner terms of the binomials: -6 * x = -6x
4. Last: Multiply the last terms of each binomial: -6 * 7 = -42

Now, combine the terms: x² + 7x - 6x - 42

Simplifying, we get: x² + x - 42

Conclusion

The expression (x-6)(x+7) is a factored form of the quadratic polynomial x² + x - 42. Understanding factoring and expanding is crucial in algebra for solving equations, simplifying expressions, and working with quadratic functions.