Concept Byte: Using Models to Multiply

Use With Lesson 8-3

ACTIVITY

You can use algebra tiles to model the multiplication of two binomials.

Activity

Find the product ( x + 4 ) ( 2 x + 3 ) . open bold italic x plus 4 close open 2 bold italic x plus 3 close .

The product is 2 x 2 + 11 x + 12 . 2 , x squared , plus 11 x plus 12 .

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2 x 2 + 3 x + 8 x + 12 2 , x squared , plus 3 x plus 8 x plus 12

2 x 2 + 11 x + 12 2 , x squared , plus 11 x plus 12  Add coefficients of like terms.

You can also model products that involve subtraction. Red tiles indicate negative variables and negative numbers.

Activity

Find the product ( x − 3 1 ) ( 2 x + 1 ) . open bold italic x minus 3 1 close open 2 bold italic x plus 1 close .

The product is 2 x 2 − x − 1 . 2 , x squared , minus x minus 1 .

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2 x 2 + x − 2 x − 1 2 , x squared , plus x minus 2 x minus 1

2 x 2 − x − 1 2 , x squared , minus x minus 1  Add coefficients of like terms.

Exercises

Use algebra tiles to find each product.

1. ( x + 4 ) ( x + 2 ) open x plus 4 close open x plus 2 close
2. ( x + 2 ) ( x − 3 ) open x plus 2 close open x minus 3 close
3. ( x + 1 ) ( 3 x − 2 ) open x plus 1 close open 3 x minus 2 close
4. ( 3 x + 2 ) ( 2 x + 1 ) open 3 x plus 2 close open 2 x plus 1 close

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