Sure, let's walk through the steps to multiply the expression [tex]\(x^2 - 2x - 3\)[/tex] by [tex]\(5x\)[/tex].
1. Write down the expressions:
- The first expression is [tex]\(x^2 - 2x - 3\)[/tex].
- The second expression is [tex]\(5x\)[/tex].
2. Apply the distributive property:
To multiply [tex]\(x^2 - 2x - 3\)[/tex] by [tex]\(5x\)[/tex], we use the distributive property, distributing [tex]\(5x\)[/tex] to each term in the polynomial [tex]\(x^2 - 2x - 3\)[/tex]:
[tex]\[
(x^2 - 2x - 3) \times 5x = (x^2 \times 5x) + (-2x \times 5x) + (-3 \times 5x)
\][/tex]
3. Perform the individual multiplications:
- Multiply the first term: [tex]\(x^2 \times 5x = 5x^3\)[/tex].
- Multiply the second term: [tex]\(-2x \times 5x = -10x^2\)[/tex].
- Multiply the third term: [tex]\(-3 \times 5x = -15x\)[/tex].
4. Combine the results:
Now, put them all together:
[tex]\[
5x^3 - 10x^2 - 15x
\][/tex]
Therefore, the product of multiplying the expression [tex]\(x^2 - 2x - 3\)[/tex] by [tex]\(5x\)[/tex] is:
[tex]\[
5x^3 - 10x^2 - 15x
\][/tex]
