Presentation on theme: "Multiplying Binomials"— Presentation transcript:
1 Multiplying Binomials 12.4LESSONMultiplying BinomialsInvestigateFind the product (3x + 1)(x + 4) using algebra tiles.1Represent each binomial using algebra tiles. Arrange the first binomial vertically and the second binomial horizontally, as shown.
2 Multiplying Binomials 12.4LESSONMultiplying BinomialsInvestigateFind the product (3x + 1)(x + 4) using algebra tiles.2The binomials define a rectangular region with length (3x + 1) units and width (x + 4) units. Fill in the region with the appropriate tiles.
3 Multiplying Binomials 12.4LESSONMultiplying BinomialsInvestigateFind the product (3x + 1)(x + 4) using algebra tiles.3The tiles covering the rectangular region represent 3x x + 4. This expression is the product of the binomials.
4 Multiplying Binomials 12.4LESSONMultiplying BinomialsInvestigateFind the product (3x + 1)(x + 4) using algebra tiles.You can also use a table to multiply two binomials. The model and table below show the product (3x + 1)(x + 4).From the table, you can see that (3x + 1)(x + 4) is 3x x + x + 4, or 3x x + 4.Terms of the first binomialx4Terms of the second binomial3x13x 212xx4Multiply terms to fill in the table. For example, 1 • x = x.
5 Multiplying Binomials 12.4LESSONMultiplying BinomialsEXAMPLE1Multiplying Binomials Using a TableFind the product (–2x + 5)(3x – 1).Write any subtractions in the binomial as additions.(–2x + 5)(3x – 1) = (–2x + 5)[3x + (–1)]First binomial3x–1Second binomial–2x5–6x 22x15x–5The product is –6x 2 + 2x + 15x – 5, or –6x x – 5.
6 Multiplying Binomials 12.4LESSONMultiplying BinomialsDistributive Property Another way to multiply binomials is to use the distributive property.
7 Multiplying Binomials 12.4LESSONMultiplying BinomialsEXAMPLE2Using the Distributive PropertyPhotograph You are enlarging a photo that is 7 inches long and 5 inches wide. The length and width of the enlargement are x times the length and width of the original photo. The enlargement will have a 2 inch mat. Write a polynomial expression for the combined area of the enlargement and mat.The total length of the enlargement and mat is (7x + 4) inches. The total width is (5x + 4) inches. To find the area, multiply.SOLUTION(7x + 4)(5x + 4) =7x(5x + 4) + 4(5x + 4)Distribute 5x + 4.= 35x x + 20x + 16Distribute 7x and 4.= 35x x + 16Combine like terms.ANSWERThe area is (35x x + 16) square inches.
8 Multiplying Binomials 12.4LESSONMultiplying BinomialsFOIL Method Notice that using the distributive property to multiply binomials produces four products that are then added. These four products are the products of the first terms, the outer terms, the inner terms, and the last terms of the binomials. You can use the shorthand FOIL to remind you of the words First, Outer, Inner, and Last.12x 2First+ 2xOuter+ 30xInner+ 5Last(2x + 5)(6x + 1) =
9 Multiplying Binomials 12.4LESSONMultiplying BinomialsEXAMPLE3Using the FOIL MethodFind the product (4x + 3)(5x – 2).First Outer Inner Last(4x)(5x)+ (4x)(–2)+ (3)(5x)+ (3)(–2)Write products of terms.20x 2+ (–8x)+ 15x+ (–6)Multiply.20x 2 + 7x – 6Combine like terms.