Question

Anyone can help me to solve this?​

Answer 1

x³ + 3x² + 2x

Explanation:

given x is the first integer then x + 1 and x + 2 are the next two integers.

the product of the first three consecutive integers is then

x(x + 1)(x + 2)

= x(x² + 2x + x + 2)

= x(x² + 3x + 2)

= x³ + 3x² + 2x

Answer 2

`x^3+3x^2+2x`

Explanation:

Definitions

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:

• x
• x + 1
• (x + 1) + 1 = x + 2

Therefore, the product of the first three consecutive integers is:

`\begin{aligned}x(x+1)(x+2) & = (x \cdot x+x \cdot 1)(x+2)\\& = (x^2+x)(x+2)\\ & = x^2 \cdot x+x^2 \cdot 2+x \cdot x+x \cdot 2\\& = x^3+2x^2+x^2+2x\\& = x^3+3x^2+2x\end{aligned}`