Question Video: Factoring an Algebraic Expression for the Surface Area | Nagwa Question Video: Factoring an Algebraic Expression for the Surface Area | Nagwa

Question Video: Factoring an Algebraic Expression for the Surface Area Mathematics • First Year of Preparatory School

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The total surface area of the square prism shown can be expressed as 8π₯Β² + 8π₯π¦. Write the factorized expression of the surface area of the square prism.

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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.

Letβs 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¦.

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