(x%2B7).jpeg "(x-9)(x+7)")
Factoring and Expanding (x-9)(x+7)
This expression represents the product of two binomials: (x-9) and (x+7). We can solve it using two main methods: factoring and expanding.
Factoring (x-9)(x+7)
Factoring is the process of breaking down an expression into simpler expressions that multiply to give the original expression. In this case, the expression is already factored, as it's presented as the product of two binomials.
Expanding (x-9)(x+7)
Expanding the expression means multiplying the two binomials together to get a single polynomial. We can use the FOIL method for this:
- First: Multiply the first terms of each binomial: x * x = x²
- Outer: Multiply the outer terms of the binomials: x * 7 = 7x
- Inner: Multiply the inner terms of the binomials: -9 * x = -9x
- Last: Multiply the last terms of each binomial: -9 * 7 = -63
Now, combine the terms:
x² + 7x - 9x - 63
Simplify by combining like terms:
x² - 2x - 63
Therefore, the expanded form of (x-9)(x+7) is x² - 2x - 63.
In summary:
- The factored form of the expression is (x-9)(x+7).
- The expanded form of the expression is x² - 2x - 63.