Distributive Law

2. Distributive Law Distributive Law: a·(b+c) = a·b+a·c where a,b,c&d represent real numbers. 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) Combining like terms = 6a - 9b +12 - 2a + 4b - 6 = 4a – 5b +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)(a2-2a+4) = a3 – 2a2 + 4a + 2a2 - 4a + 8 = a3 + 8 Answer :a3 + 8 Return to table or click anywhere to continue.

3. Example 3: Simplify (x2 +1)(x + 1) – x(x + 2)(x - 1) (x2 +1)(x + 1) – x (x + 2)(x - 1) Applying the Distributive Law … = [ x3 + x2 + x + 1] – x [x2 - x +2x- 2] Working on the parentheses … = [ x3 + x2 + x + 1 ] – x [x2 + x - 2] Removing parentheses …. = x3 + x2 + x + 1 – x3 – x2 + 2x Combining like terms … = 3x + 1 Answer : 3x + 1 Example 4: Simplify Applying the Distributive Law, we get: Simplifying … Expanding … Removing parenthesis … Combining like terms Click Here to see factoring polynomials. Return to table Answer4x2-3x+5