Question Video: Finding the Area of a Rectangle by Expanding the Product of Two Binomials Mathematics • 9th Grade

Find the area of a rectangle that has a width of 𝑥 − 5𝑦 cm and a length of 𝑥 + 4𝑦 cm.

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Video Transcript

Find the area of a rectangle that has a width of 𝑥 minus five 𝑦 centimeters and a length of 𝑥 plus four 𝑦 centimeters.

We’ve been given algebraic expressions for the length and width of a rectangle and asked to find an expression for its area. The area of a rectangle is equal to the product of its dimensions. So we can find an expression for the area of this rectangle by multiplying the expressions for its length and width together. Doing so gives 𝑥 plus four 𝑦 multiplied by 𝑥 minus five 𝑦. We now have the product of two binomials, which we need to simplify by distributing the parentheses.

There are a number of different methods we can use to do this, such as the vertical method or grid method. We’ll use the horizontal method, in which we distribute one of the binomial factors over the other. Multiplying the second binomial by each term in the first binomial gives 𝑥 multiplied by 𝑥 minus five 𝑦 plus four 𝑦 multiplied by 𝑥 minus five 𝑦. We then distribute each of the linear factors over the binomial, giving 𝑥 squared minus five 𝑥𝑦 from the first part of the expression and then plus four 𝑥𝑦 minus 20𝑦 squared from the second part.

Finally, we can simplify this expression one stage further by combining the like terms of negative five 𝑥𝑦 and positive four 𝑥𝑦 to give negative 𝑥𝑦. By multiplying the two binomials together, we found that the area of the given rectangle is 𝑥 squared minus 𝑥𝑦 minus 20𝑦 squared square centimeters.

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