Question Video: Multiplying a Binomial and a Trinomial to Find the Volume of a Prism | Nagwa Question Video: Multiplying a Binomial and a Trinomial to Find the Volume of a Prism | Nagwa

# Question Video: Multiplying a Binomial and a Trinomial to Find the Volume of a Prism Mathematics • First Year of Preparatory School

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A rectangular prism has its base area given by the trinomial (2π₯Β² + 7π₯π¦ + 2π¦Β²) cmΒ² and its height given by the binomial (π₯ + π¦) cm. Find its volume.

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### Video Transcript

A rectangular prism has its base area given by the trinomial two π₯ squared plus seven π₯π¦ plus two π¦ squared centimeters squared and its height given by the binomial π₯ plus π¦ centimeters. Find its volume.

In this question, we have been asked to find the volume of a rectangular prism. So letβs start by recalling the formula for the volume of a prism. We have that the volume of a prism is equal to the area of its base multiplied by its height. Weβve been told in the question that the area of the base of the prism is two π₯ squared plus seven π₯π¦ plus two π¦ squared centimeters squared and that its height is π₯ plus π¦ centimeters.

We can see that the volume π£ is equal to the product of a binomial and a trinomial. We can use the distributive property of multiplication over addition to distribute the binomial term over each of the trinomial terms. We now have three products of monomials and binomials, which we can distribute. And now we have completely expanded the parentheses. We may notice that there are some like terms, which we can combine.

Now that we have combined these like terms, we cannot simplify the right-hand side anymore. Since the area is given in centimeters squared and the height is given in centimeters, we have that the volume will be in centimeters cubed. Hence, we can say that the volume of the prism is two π₯ cubed plus nine π₯ squared π¦ plus nine π₯π¦ squared plus two π¦ cubed centimeters cubed.

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