To expand the expression [tex]\((x+8)(x-3)\)[/tex] using the distributive property, follow these steps:
1. Apply the distributive property (FOIL Method):
- First: Multiply the first terms in each binomial.
- Outer: Multiply the outer terms.
- Inner: Multiply the inner terms.
- Last: Multiply the last terms in each binomial.
Let's break it down:
First: Multiply the first terms in each binomial:
[tex]\[ x \times x = x^2 \][/tex]
Outer: Multiply the outer terms:
[tex]\[ x \times -3 = -3x \][/tex]
Inner: Multiply the inner terms:
[tex]\[ 8 \times x = 8x \][/tex]
Last: Multiply the last terms:
[tex]\[ 8 \times -3 = -24 \][/tex]
2. Combine like terms:
- Combine the [tex]\(x \)[/tex] terms: [tex]\(-3x + 8x = 5x\)[/tex]
- The constant term is [tex]\(-24\)[/tex]
So, the expanded form of [tex]\((x+8)(x-3)\)[/tex] is:
[tex]\[ x^2 + 5x - 24 \][/tex]
Thus, the completed expression is:
[tex]\[ x^2 + 5x - 24 \][/tex]
