lindsay is calculating the product of two consecutive odd integers. she says that the product is always…

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.\nis lindsays statement true? use the drop - down menus to explain your answer.\nclick the arrows to choose an answer from each menu.\ntwo consecutive odd integers can be represented as x and x + 2. the product of the two integers, x(x + 2), is choose...\nthe 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.\nlindsays statement is choose...

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.\nis lindsays statement true? use the drop - down menus to explain your answer.\nclick the arrows to choose an answer from each menu.\ntwo consecutive odd integers can be represented as x and x + 2. the product of the two integers, x(x + 2), is choose...\nthe 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.\nlindsays statement is choose...

Answer

Explanation:

Step1: Expand the product of two consecutive odd - integers

Let the two consecutive odd integers be $x$ and $x + 2$. Then $x(x + 2)=x^{2}+2x$.

Step2: Find the even integer between the odd integers

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

Step3: Square the even integer and subtract 1

$(x + 1)^{2}-1=(x^{2}+2x + 1)-1=x^{2}+2x$.

Step4: Compare the two results

Since $x(x + 2)=x^{2}+2x$ and $(x + 1)^{2}-1=x^{2}+2x$, the product of two consecutive odd integers is equal to the square of the even integer between them minus 1.

Answer:

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