Video: The Distributive Property of Multiplication

The diagram shows a rectangle of sides 𝑎 + 𝑏 and 𝑐 + 𝑑. Its area is thus (𝑎 + 𝑏) × (𝑐 + 𝑑), which can also be written as (𝑎 + 𝑏) (𝑐 + 𝑑). Work out the area of the smaller rectangles that make up the bigger rectangle to find an equivalent expression to (𝑎 + 𝑏) (𝑐 + 𝑑).

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Video Transcript

The diagram shows a rectangle of sides 𝑎 plus 𝑏 and 𝑐 plus 𝑑. Its area is thus 𝑎 plus 𝑏 times 𝑐 plus 𝑑, which can also be written as 𝑎 plus 𝑏 times 𝑐 plus 𝑑. Work out the area of the smaller rectangles that make up the bigger rectangle to find an equivalent expression to 𝑎 plus 𝑏 times 𝑐 plus 𝑑.

The larger rectangle is made up of four smaller rectangles. We need to find the expression for each of these areas. The area of the piece shaded in blue is equal to 𝑎 times 𝑐, length times width. The second rectangle, 𝑎 times 𝑑. The third rectangle, area is equal to 𝑏 times 𝑐. And the fourth rectangle has an area of 𝑏 times 𝑑.

To find the area of the larger rectangle, we’ll need to add all four of these pieces together, 𝑎𝑐 plus 𝑎𝑑 plus 𝑏𝑐 plus 𝑏𝑑 is an equivalent expression to 𝑎 plus 𝑏 times 𝑐 plus 𝑑.

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