(x%5E2%2B7x-8).jpeg "(x-4)(x^2+7x-8)")
Expanding the Expression (x-4)(x^2+7x-8)
This expression involves the multiplication of a binomial (x-4) and a trinomial (x^2+7x-8). To expand this, we can use the distributive property, also known as the FOIL method.
FOIL stands for First, Outer, Inner, Last. This helps us remember to multiply each term in the first expression by each term in the second expression.
Let's break down the steps:
1. First:
- Multiply the first terms of each expression:
- x * x^2 = x^3
2. Outer:
- Multiply the outer terms of the expressions:
- x * -8 = -8x
3. Inner:
- Multiply the inner terms of the expressions:
- -4 * x^2 = -4x^2
4. Last:
- Multiply the last terms of the expressions:
- -4 * -8 = 32
Now, we combine all the terms:
x^3 - 8x - 4x^2 + 32
Finally, we arrange the terms in descending order of their exponents:
x^3 - 4x^2 - 8x + 32
Therefore, the expanded form of (x-4)(x^2+7x-8) is x^3 - 4x^2 - 8x + 32.