1. Distributive Law Example 1Example 2 Example 3Example 4

2. Distributive Law Using this law from left to right we can remove the parenthesis and then simplify the algebraic expression; and if we use it from right to left, we can factor algebraic expressions. Example1: Simplify 3 ( 2a - 3b + 4 ) – 2 (a – 2b + 3) Expanding … 3 ( 2a - 3b + 4 ) – 2 ( a – 2b + 3) = 6a- 9b+12- 2a + 4b - 6 Answer: 4a – 5b + 6 General Distributive Law: (a+b+c+…)(p+q+r+…)= a(p+q+r+ …) + b(p+q+r+ …)+ c (p+q+r+ …)+ … = ap+aq+ar+… + bp+bq+br… + cp+cq+cr+ …+ … Example 2: Simplify (a+2)(a 2 -2a+4) = a 3 – 2a 2 + 4a+ 2a 2 - 4a+ 8 Answer : a 3 + 8 Distributive Law: a·(b+c) = a·b+a·c where a,b,c&d represent real numbers. = 4a – 5b +6Combining like terms = a 3 + 8 Return to tableReturn to table or click anywhere to continue.

3. Example 3: Simplify (x 2 +1)(x + 1) – x(x + 2)(x - 1) (x 2 +1)(x + 1) – x (x + 2)(x - 1) Applying the Distributive Law … = [ x 3 + x 2 + x + 1] – x [x 2 - x +2x - 2] Working on the parentheses … = [ x 3 + x 2 + x + 1 ] – x [x 2 + x - 2] Removing parentheses …. = x 3 + x 2 + x + 1 – x 3 – x 2 + 2x Combining like terms … = 3x + 1 Example 4: Simplify Applying the Distributive Law, we get: Simplifying … Expanding … Removing parenthesis … Answer 4x 2 -3x+5 Click Here to see factoring polynomials. Return to tableHere Return to table Combining like terms Answer : 3x + 1