Answer:
[tex] \large \bold{x^3+3x^2+2x} \\ [/tex]
Step-by-step explanation:
[tex]\\\large\underline{\sf{\blue{Definitions : }}} \\ [/tex]
Integer: A whole number that can be positive, negative, or zero.
Consecutive Integers: Integers that follow each other continuously in the order from smallest to largest.
Product: The result of multiplying two of more values together.
Let x be the first integer.
Therefore, to find the consecutive integers, add 1 to each term:
- [tex] \bold{x} \\ [/tex]
- [tex] \bold{x + 1} \\ [/tex]
- [tex] \bold{(x + 1) + 1 = x + 2} \\ [/tex]
Therefore, the product of the first three consecutive integers is:
[tex]\begin{gathered}\begin{aligned} \sf{x(x+1)(x+2)} & \implies \sf{(x \cdot x+x \cdot 1)(x+2)}\\& \implies \sf{(x^2+x)(x+2)}\\ & \implies \sf{x^2 \cdot x+x^2 \cdot 2+x \cdot x+x \cdot 2}\\& \implies \sf{ x^3+2x^2+x^2+2x}\\& \implies \bold{x^3+3x^2+2x}\\\end{aligned}\end{gathered} [/tex]
