D. Binomial Multiplication
D. Binomial Multiplication
Binomials can be multiplied using the distributive property. Sometimes this process is referred to as 'expanding'. To determine the final product, multiply each term in the first binomial by each term in the second binomial. When multiplying two binomials,
you will have four simpler products. Three ways of representing this process are shown.
Strategy 1: Grid Multiplication with Algebra Tiles
To multiply two binomials using algebra tiles, place one binomial vertically to represent the width, and the other horizontally to represent the length. Fill in the area of the resulting rectangle to determine the product.
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Example 1 |
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Use algebra tiles to multiply «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mn»2«/mn»«mi»r«/mi»«mo»-«/mo»«mn»4«/mn»«mo»)«/mo»«mo»(«/mo»«mo»-«/mo»«mi»r«/mi»«mo»+«/mo»«mn»3«/mn»«mo»)«/mo»«/math». Place tiles representing «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn mathcolor=¨#B94A48¨»2«/mn»«mi mathcolor=¨#B94A48¨»r«/mi»«mo mathcolor=¨#B94A48¨»-«/mo»«mn mathcolor=¨#B94A48¨»4«/mn»«/math» horizontally (length) and «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#B94A48¨»-«/mo»«mi mathcolor=¨#B94A48¨»r«/mi»«mo mathcolor=¨#B94A48¨»+«/mo»«mn mathcolor=¨#B94A48¨»3«/mn»«/math» vertically (width).
Represent the product of «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn mathcolor=¨#B94A48¨»2«/mn»«mi mathcolor=¨#B94A48¨»r«/mi»«/math» and «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#B94A48¨»-«/mo»«mi mathcolor=¨#B94A48¨»r«/mi»«/math» by filling in the appropriate area. «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#B94A48¨»(«/mo»«mn mathcolor=¨#B94A48¨»2«/mn»«mi mathcolor=¨#B94A48¨»r«/mi»«mo mathcolor=¨#B94A48¨»)«/mo»«mo mathcolor=¨#B94A48¨»(«/mo»«mo mathcolor=¨#B94A48¨»-«/mo»«mi mathcolor=¨#B94A48¨»r«/mi»«mo mathcolor=¨#B94A48¨»)«/mo»«mo mathcolor=¨#B94A48¨»=«/mo»«mo mathcolor=¨#B94A48¨»-«/mo»«mn mathcolor=¨#B94A48¨»2«/mn»«msup mathcolor=¨#B94A48¨»«mi mathcolor=¨#B94A48¨»r«/mi»«mn»2«/mn»«/msup»«/math» Remember that a positive value multiplied by a negative value results in a negative value.
Represent the product of «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#B94A48¨»-«/mo»«mn mathcolor=¨#B94A48¨»4«/mn»«/math» and «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#B94A48¨»-«/mo»«mi mathcolor=¨#B94A48¨»r«/mi»«/math» by filling in the appropriate area. «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#B94A48¨»(«/mo»«mo mathcolor=¨#B94A48¨»-«/mo»«mn mathcolor=¨#B94A48¨»4«/mn»«mo mathcolor=¨#B94A48¨»)«/mo»«mo mathcolor=¨#B94A48¨»(«/mo»«mo mathcolor=¨#B94A48¨»-«/mo»«mi mathcolor=¨#B94A48¨»r«/mi»«mo mathcolor=¨#B94A48¨»)«/mo»«mo mathcolor=¨#B94A48¨»=«/mo»«mn mathcolor=¨#B94A48¨»4«/mn»«mi mathcolor=¨#B94A48¨»r«/mi»«/math»
Represent the product of «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn mathcolor=¨#B94A48¨»2«/mn»«mi mathcolor=¨#B94A48¨»r«/mi»«/math» and 3 by filling in the appropriate area. «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#B94A48¨»(«/mo»«mn mathcolor=¨#B94A48¨»2«/mn»«mi mathcolor=¨#B94A48¨»r«/mi»«mo mathcolor=¨#B94A48¨»)«/mo»«mo mathcolor=¨#B94A48¨»(«/mo»«mn mathcolor=¨#B94A48¨»3«/mn»«mo mathcolor=¨#B94A48¨»)«/mo»«mo mathcolor=¨#B94A48¨»=«/mo»«mn mathcolor=¨#B94A48¨»6«/mn»«mi mathcolor=¨#B94A48¨»r«/mi»«/math»
Represent the product of «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#B94A48¨»-«/mo»«mn mathcolor=¨#B94A48¨»4«/mn»«/math» and 3 by filling in the appropriate area. «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#B94A48¨»(«/mo»«mo mathcolor=¨#B94A48¨»-«/mo»«mn mathcolor=¨#B94A48¨»4«/mn»«mo mathcolor=¨#B94A48¨»)«/mo»«mo mathcolor=¨#B94A48¨»(«/mo»«mn mathcolor=¨#B94A48¨»3«/mn»«mo mathcolor=¨#B94A48¨»)«/mo»«mo mathcolor=¨#B94A48¨»=«/mo»«mo mathcolor=¨#B94A48¨»-«/mo»«mn mathcolor=¨#B94A48¨»12«/mn»«/math»
There are two «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#B94A48¨»-«/mo»«msup mathcolor=¨#B94A48¨»«mi mathcolor=¨#B94A48¨»x«/mi»«mn»2«/mn»«/msup»«/math» tiles, ten «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathcolor=¨#B94A48¨»x«/mi»«/math» tiles, and twelve −1 tiles, so «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#B94A48¨»(«/mo»«mn mathcolor=¨#B94A48¨»2«/mn»«mi mathcolor=¨#B94A48¨»r«/mi»«mo mathcolor=¨#B94A48¨»-«/mo»«mn mathcolor=¨#B94A48¨»4«/mn»«mo mathcolor=¨#B94A48¨»)«/mo»«mo mathcolor=¨#B94A48¨»(«/mo»«mo mathcolor=¨#B94A48¨»-«/mo»«mi mathcolor=¨#B94A48¨»r«/mi»«mo mathcolor=¨#B94A48¨»+«/mo»«mn mathcolor=¨#B94A48¨»3«/mn»«mo mathcolor=¨#B94A48¨»)«/mo»«mo mathcolor=¨#B94A48¨»=«/mo»«mo mathcolor=¨#B94A48¨»-«/mo»«mn mathcolor=¨#B94A48¨»2«/mn»«msup mathcolor=¨#B94A48¨»«mi mathcolor=¨#B94A48¨»r«/mi»«mn»2«/mn»«/msup»«mo mathcolor=¨#B94A48¨»+«/mo»«mn mathcolor=¨#B94A48¨»10«/mn»«mi mathcolor=¨#B94A48¨»r«/mi»«mo mathcolor=¨#B94A48¨»-«/mo»«mn mathcolor=¨#B94A48¨»12«/mn»«/math» |
