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.
