Question Video: Using an Area Model to Multiply Polynomials | Nagwa Question Video: Using an Area Model to Multiply Polynomials | Nagwa

# Question Video: Using an Area Model to Multiply Polynomials

Use an area model to write an expression equivalent to (2𝑥 − 7)(−3𝑦 + 2𝑥).

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### Video Transcript

Use an area model to write an expression equivalent to two 𝑥 minus seven multiplied by negative three 𝑦 plus two 𝑥.

The expressions two 𝑥 minus seven and negative three 𝑦 plus two 𝑥 have been split into their two terms. We know that in order to calculate the area of a rectangle, we multiply the length by the width. This means that to calculate the area of the top-left rectangle, we multiply two 𝑥 by negative three 𝑦. Multiplying a positive by a negative gives a negative. Therefore, two 𝑥 multiplied by negative three 𝑦 is negative six 𝑥𝑦.

The top-right section is a square. We are multiplying two 𝑥 by two 𝑥. This is equal to four 𝑥 squared. For the bottom-left rectangle, we need to multiply negative seven by negative three 𝑦. Multiplying two negative terms gives a positive answer, so this is equal to 21𝑦. Finally, we need to multiply negative seven by two 𝑥. This is equal to negative 14𝑥.

The total area of the whole rectangle will be equal to the sum of these four terms. This means that two 𝑥 minus seven multiplied by negative three 𝑦 plus two 𝑥 is equivalent to negative six 𝑥𝑦 plus four 𝑥 squared plus 21𝑦 minus 14𝑥. These four terms can be written in any order.

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