Final answer:
And that's the result of the multiplication of the given polynomials. The expanded form of \( (x + 3)(x - 4) \) is \( x^2 - x - 12 \).
Step-by-step explanation:
To multiply the polynomial expressions (x + 3) and (x - 4), we will use the distributive property (also known as the FOIL method, which stands for First, Outer, Inner, Last). This method involves multiplying each term in the first polynomial by each term in the second polynomial.
Here's how it works step by step:
Given two binomials (x + 3) and (x - 4), let's apply the FOIL method:
1. **First:** Multiply the first terms in each binomial:
\( x \times x = x^2 \)
2. **Outer:** Multiply the outer terms in the product:
\( x \times (-4) = -4x \)
3. **Inner:** Multiply the inner terms:
\( 3 \times x = 3x \)
4. **Last:** Multiply the last terms in each binomial:
\( 3 \times (-4) = -12 \)
Now, combine all these results:
\( x^2 \) (from the First step)
\( -4x \) (from the Outer step)
\( +3x \) (from the Inner step)
\( -12 \) (from the Last step)
Combine like terms:
\( x^2 - 4x + 3x - 12 \)
\( x^2 - x - 12 \)
And that's the result of the multiplication of the given polynomials. The expanded form of \( (x + 3)(x - 4) \) is \( x^2 - x - 12 \).