Sure, let's solve the given expression step-by-step:
Given expression:
[tex]\[ (2x - 3)(x + 5) \][/tex]
We will use the distributive property (also known as the FOIL method for binomials) to expand this expression.
1. First, distribute [tex]\(2x\)[/tex] in [tex]\(2x - 3\)[/tex] to each term in [tex]\(x + 5\)[/tex]:
[tex]\[ 2x \cdot x + 2x \cdot 5 \][/tex]
which simplifies to:
[tex]\[ 2x^2 + 10x \][/tex]
2. Next, distribute [tex]\(-3\)[/tex] in [tex]\(2x - 3\)[/tex] to each term in [tex]\(x + 5\)[/tex]:
[tex]\[ -3 \cdot x - 3 \cdot 5 \][/tex]
which simplifies to:
[tex]\[ -3x - 15 \][/tex]
3. Combine all the terms from the two distributive steps:
[tex]\[ 2x^2 + 10x - 3x - 15 \][/tex]
4. Now, combine like terms:
[tex]\[ 2x^2 + (10x - 3x) - 15 \][/tex]
which simplifies to:
[tex]\[ 2x^2 + 7x - 15 \][/tex]
So, the expanded form of the given expression [tex]\((2x - 3)(x + 5)\)[/tex] is:
[tex]\[ 2x^2 + 7x - 15 \][/tex]
