Mastering Polynomial Multiplication Techniques
Learn to multiply binomials using properties like the distributive property and the FOIL method. Practice multiplying binomials and trinomials step-by-step with helpful examples. Enhance your algebra skills and boost your problem-solving abilities in polynomial multiplication.
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Presentation Transcript
7.2 Multiplying Polynomials 1. Students will be able to multiply binomials. 2. Students will be able to use the FOIL method. 3. Students will be able to multiply binomials and trinomials.
1. Multiplying Binomials using the Distributive Property. ( 2)( 5) x x + + + + = + + + ( 2 )( 5) ( 5) 2 ( 5 ) x x x x x = + + + ( ) x (5) 2( ) (5) 2 x x x = + + + 2 5 2 10 x x x = + + 2 7 10 x x
1. Multiplying Binomials using a Table. (2 3)( x + 5) x 2x -3 x 2x2 -3x +5 +10x -15 + 2 2 3 10 15 x x x + 2 2 7 15 x x
You Try! With Distributive Property! + ( 2)( 6) z z + = + + ( 2 )( 6) ( 6 ) 2 ( 6 ) z z z z z = + ( ) z (6) ( ) 2 2 ) (6 z z z = + 2 6 2 12 z z z = + 2 4 12 z z
You Try! With a Table! ( 5)(2 1) r r r -5 2r 2r2 -10r -1 -1r +5 = + 2 2 10 1 5 r r r = + 2 2 11 5 r r
2. Using the FOIL Method ( ( 3)( 3)( 6) 6) x x x x ( 3)( 6) = x x 2 ( ) x x x First terms ) 6 = ( 6 x x ( 3)( 6) x x Outer terms ( ) 3 = 3 x x ( 3 )( 6) x x Inner terms 3 6 = + ( ) 18 ( 3 )( 6) x x Last terms ( 3)( 6) x x = + = x + 2 2 9 18 6 3 18 x x x x
2. Using the FOIL Method + (2 1)(3 5) x x Last First Outer Inner + = 2 ( 5) x + 1(3 ) x + 1( 5) + (2 1)(3 5) 2 (3 ) x x x x = + 2 6 10 3 5 x x x = 2 6 7 5 x x
You Try! Using the FOIL Method! Last Inner First Outer + = 4 (2) x + 7(3 ) x 7(2) (4 7)(3 2) 4 (3 ) x x x x = + 2 12 8 21 14 x x x = 2 12 13 14 x x
3. Multiplying a Binomial and a Trinomial + 2 ( 5)( 3 2) x x x Using the Distributive Property + = + 2 2 2 ( 5)( 3 2 ) ( 3 2) 5 ( 3 2 ) x x x x x x x x = + ( 3 ) + ( 2) + + ( 3 ) ( 5 2) + 2 2 ( ) 5 ( ) 5 x x x x x x x = + 3 2 2 3 2 5 15 10 x x x x x = + 3 2 2 17 10 x x x
Last One YEH!! But First Let us review what we learned today 1. Students will be able to multiply binomials. 2. Students will be able to use the FOIL method. 3. Students will be able to multiply binomials and trinomials.
Last One + + 2 ( 6)(2 7) x x x + + = + + + 2 2 2 ( 6 )(2x 7) (2 7 ) 6 (2 7) x x x x x x x = + + + + ( 6 7) + 2 2 (2 ) ( ) (7) 6 (2 ) 6 ( ) x x x x x x x = + + + 3 2 2 2 7 12 6 42 x x x x x = + + + 3 2 2 11 42 x x x Good Job!
