Question

lindsay is calculating the product of two consecutive odd integers. she says that the product is always equal to the square of the even integer between them minus 1.
is lindsays statement true? use the drop - down menus to explain your answer.
click the arrows to choose an answer from each menu.
two consecutive odd integers can be represented as $x$ and $x + 2$. the product of the two integers, $x(x + 2)$, is choose...
the even integer between the odd integers is represented by the expression choose.... this expression squared, minus 1 is choose... the product of the consecutive odd numbers.
lindsays statement is choose...

Explanation:

Step1: Expand the product

$x(x+2) = x^2 + 2x$

Step2: Define middle even integer

The even integer between $x$ and $x+2$ is $x+1$.

Step3: Compute square minus 1

$(x+1)^2 - 1 = x^2 + 2x + 1 - 1 = x^2 + 2x$

Step4: Compare the two expressions

Both simplify to $x^2 + 2x$, so they are equal.

Answer:

1. The product of the two integers, $x(x+2)$, is $\boldsymbol{x^2 + 2x}$
2. The even integer between the odd integers is represented by the expression $\boldsymbol{x+1}$
3. This expression squared, minus 1 is $\boldsymbol{equal\ to}$ the product of the consecutive odd numbers.
4. Lindsay's statement is $\boldsymbol{true}$