Distributive Property
By the end of this lesson, you will know how to simplify expressions by using the distributive property.
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We know that multiplication is distribution over addition and subtraction. We often use this distributive property when doing 'mental' arithmetic.
Examples: 3 x 29 cents = 3 x (20 + 9) = (3 x 20) + (3 x 9) = 60 + 27 = 87 cents or 3 x 29 cents = 3 x (30 - 1) = (3 x 30) - (3 x 1) = 90 - 3 = 87 cents In algebra, the distributive property is used to remove the parentheses. with rods and cubes: Example: 3 ( n + 4 ) = 3 ( l . . . . ) = 3 ( l ) + 3 ( . . . . ) = l l l . . . . . . . . Use the rods and cubes to remove the parentheses on the following problems. Draw a picture of your answers. 1) 2 ( n + 3 ) 2) 3 (n - 2) 3) 2 ( n - 1 ) 4) 4 ( n + 1 ) 5) 2 ( 2n - 1 ) 6) (2n + 3) 2 Can you find the pattern for removing parentheses in each problem? a) 3 x ( 20 + 5 ) b) 2 x ( 50 - 1 ) c) a ( b + c ) Classwork:
1) 5 ( a + 3) 2) 4 ( n - 4) 3) 5 ( b + 3) 4) 6 (x - 4) 5) 7 ( 2 + a) 6) 6 ( 3 - x) 7) 9 (3 - n) 8) 8 ( b + 8 ) 9) 4 ( 2a + 3 ) 10) 5 ( 3b - 6 ) 11) 2 ( 3n - 4 ) 12) 1/3 ( 12x - 9) 13) 2 (x + 3) + x 14) 5 ( x - 3 ) - 4x 15) 7 + 2 (x + 4)
16) 3 ( x + 4) - 2 17) 4 ( x - 3 ) + 10 18) 4 (2x - 3 ) + 20 19) 2n + 4 ( n + 1 ) 20) 3 + 2 ( 5n - 6 ) 21) 4 ( n + 5 ) - 7 22) 2 ( 7 - n ) + 3 n 23) 3 ( n + 2 ) - n 24) 4 ( n - 1 ) + (2) (3) 25) 3 ( n + 2 ) - ( 2 ) ( 2 ) 26) 2 ( n + 2 ) + 3 ( n - 1 ) 27) 3 ( n - 1 ) - 2 ( n + 2 ) 28) 1/2 ( 6x + 10 ) - x 29) 1/3 ( 3x - 9 ) + 2x 30) 1/4 ( 20 - 8x ) + 5x |
