Question Video: Using an Area Model to Multiply Polynomials Mathematics

Use the area model to write an expression equivalent to 3𝑎(𝑏 + 2𝑐 − 𝑑).

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Video Transcript

Use the area model to write an expression equivalent to three 𝑎 multiplied by 𝑏 plus two 𝑐 minus 𝑑.

We notice in our model that the expression 𝑏 plus two 𝑐 minus 𝑑 has been split into its three terms 𝑏, two 𝑐, and negative 𝑑. We recall that in order to find the area of any rectangle, we multiply the length by the width. This means that the area of the first section will be equal to three 𝑎 multiplied by 𝑏. This is equal to three 𝑎𝑏.

We calculate the area of the middle or second section by multiplying three 𝑎 by two 𝑐. Three multiplied by two is equal to six, so three 𝑎 multiplied by two 𝑐 is six 𝑎𝑐. Finally, we need to multiply three 𝑎 by negative 𝑑. This is equal to negative three 𝑎𝑑. We can, therefore, calculate the area of the whole rectangle by finding the sum of these three terms. Three 𝑎 multiplied by 𝑏 plus two 𝑐 minus 𝑑 is equal to three 𝑎𝑏 plus six 𝑎𝑐 minus three 𝑎𝑑.

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