Factoring Special Products in Algebra
Learn how to factor the difference of two squares and perfect square trinomials using special product patterns in algebra. Explore examples and shortcuts to master factoring techniques for efficient problem-solving.
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7.7 Factoring Special Products 1. Students will be able to factor the difference of two squares. 2. Students will be able to factor perfect square trinomials. This will be very similar to 7.5 and 7.6. And you can do all the problems like 7.5 and 7.6 and not learn anything new. Or you can learn the short cuts for the special products.
1. Students will be able to factor the difference of two squares. Difference of two squares pattern = a b a b + 2 2 2 2 ( )( ) a a b b Example = = = + x x x 2 2 2 2 2 2 2 9 9 9 3 3 ( 3)( 3) x x x x = = = + 2 2 2 2 2 2 2 x x x 25 25 25 5 5 ( 5)( 5) x x x x = = = + 2 2 2 2 2 2 2 4 4 4 1 1 1 (2 ) (2 ) 1 1 (2 1)(2 1) z z z z z z z
Lets do two more of difference of two squares. Difference of two squares pattern = a b a b + 2 2 2 2 ( )( ) a a b b Examples = + 2 2 n n 9 9 16 16 (3 4)(3 4) n n = + 2 2 h h 16 16 49 49 (4 7)(4 7) h h
2. Students will be able to factor perfect square trinomials. Perfect Square Trinomial Pattern + + + ab b + ab b + ab b + = = a b a b + a b a b + + + = a b + 2 2 2 2 2 2 2 2 2 2 ( ( )( )( ) ) ( ) a a a And ab b + ab b + ab b + = = a b a b a b a b = a b 2 2 2 2 2 2 2 2 2 2 ( ( )( )( ) ) ( ) a a a Examples + + + + + = + = + + + + = + 2 2 2 2 2 2 2 2 6 6 6 9 9 9 2( )(3) 3 x 2( )(3) 3 x ( 3) x x x x x x x x x + + + = = + + = 2 2 2 2 2 2 2 2 8 8 8 16 16 16 2( )(4) 4 x 2( )(4) 4 x x x x x x x x x ( 4) x
Lets do a few more examples. Perfect Square Trinomial Pattern + ab b + = a b + ab b + = a b 2 2 2 2 2 2 and 2 ( ) 2 ( ) a a Examples 2(2 )(3) 3 x 2(2 )(3) 3 x + + + + + = + = + + + + = + 2 2 2 2 2 2 2 2 4 4 4 12 12 12 9 9 9 (2 ) (2 ) (2 3) x x x x x x x x x + + + + = = = + + + = = + + = 2 2 2 2 2 2 2 2 2 2 2 2 9 9 9 9 36 36 36 36 36 36 36 36 9( 9( 9( 4 4 4 4) 4) 4) 9[ 9[ 2( )(2) 2 ] x 2( )(2) 2 ] x 9( 2) x x x x x x x x x x x x x x x x x Don t forget to look for a GCF!! + + + = = + + = 2 2 2 2 2 2 2 2 28 28 28 196 196 196 x x x x x x 2( )(14) 14 x 2( )(14) 14 x x x ( 14) x
You Try!!! Factor. 60 x x + + 2 2 + 49 81 9 100 2 x 16 40 25 x x + + + 2 2 2 2 (3 ) 2(3 )(10) 10 x (4 ) 2(4 )(5) 5 x x x 2 2 (7 ) 9 x x 2 x+ (4 5) 2 + (3 10) (7 9)(7 9) x x
Last three But First Let us review what we learned today 1. Students will be able to factor the difference of two squares. 2. Students will be able to factor perfect square trinomials.
Last three Factor. x + + + 2 2 2 25 36 9 24 16 24 144 x x x x + + 2 2 + 2( )(12) 12 x x 2 2 (3 ) 2(3 )(4) 4 x x 2 2 (5 ) 6 x + x+ (5 6)(5 6) x x 2 x ( 12) 2 (3 4) Good Job!
