Video Transcript
The total surface area of the square prism shown can be expressed as eight π₯ squared plus eight π₯π¦. Write the factorized expression of the surface area of the square prism.
In this question, we are given the expression for the surface area of a given square prism and asked to factor the expression fully. To do this, we need to find all of the common factors among the terms.
Letβs start by checking for integer factors. We can see that both terms have a factor of eight. So we can take this factor out of both terms. We can also check for factors among the variables. We know that π₯ squared is π₯ times π₯. So both terms share a factor of π₯. We can also note that the first term does not have a factor of π¦. So we cannot take out a factor of π¦.
We call eight π₯ the greatest common factor of the two terms, since we cannot take out any further factors. We see that the surface area of the square prism is equal to eight π₯ multiplied by π₯ plus π¦. We cannot factor the expression any further. Hence, the fully factored expression for the surface area of the given square prism is eight π₯ multiplied by π₯ plus π¦.
