Step 2: Substitute back into the original expression and put each expression in parentheses b2 b 6 * b 2 = (b 3)(b + 2) * (b 2) – – – – – b2 4b + 4 b 3 (b 2)(b 2) (b 3) – – – – – [in this case (b 3) & (b 2)] Step 3: Cancel out anything that is the same on the top and bottom lines – – (b 3)(b + 2) * (b 2) Finally down what is left over: (b + 2) and this is the final answer. – – (b 2)(b 2) (b 3) (b 2) – – – – B) Dividing algebraic fractions The only difference between multiplying and dividing algebraic expressions is that when dividing the first step is to the second expression (multiply by the reciprocal) ‘flip’ Example 2 Simplify u2 3u 10 ÷ u2 10u + 25 – – – u 2 u - 5 – Step 1 : Because we are dividing the first step is to flip the second part of the expression u2 3u 10 ÷ u2 10u + 25 = u2 3u 10 * u 5__ – – – – – – u 2 u 5 u 2 u2 10u + 25 – – – – Now follow the steps for multiplying: Factor each expression: u2 3u 10 = (u 5)(u + 2) and u2 10u + 25 = (u 5)(u 5) – – – – – – Substitute: u2 3u 10 * u 5__ = (u 5)(u + 2) * (u 5)_ – – – – – u 2 u2 10u + 25 (u 2) (u 5)(u 5) – – – – – Cancel: (u 5)(u + 2) * (u 5)___ = (u + 2) and this is the final answer. – – (u 2) (u 5)(u 5) (u 2) – – – – Regents Questions Q1 (Jan 09 Q35) Q2 (Aug 09 Q37) Q3 (June 10 Q37)
Step 2: Substitute back into the original expression and put each expression in parentheses b2 – b – 6 * b – 2 = (b – 3)(b + 2) * (b – 2) b2 – 4b + 4 b – 3 (b – 2)(b – 2) (b – 3) Step 3: Cancel out anything that is the same on the top and bottom lines [in this case (b – 3) & (b – 2)] (b – 3)(b + 2) * (b – 2) Finally down what is left over: (b + 2) and this is the final answer. (b – 2)(b – 2) (b – 3) (b – 2) B) Dividing algebraic fractions The only difference between multiplying and dividing algebraic expressions is that when dividing the first step is to ‘flip’ the second expression (multiply by the reciprocal) Example 2 Simplify u2 – 3u – 10 ÷ u2 – 10u + 25 u – 2 u - 5 Step 1 : Because we are dividing the first step is to flip the second part of the expression u2 – 3u – 10 ÷ u2 – 10u + 25 = u2 – 3u – 10 * u – 5__ u – 2 u – 5 u – 2 u2 – 10u + 25 Now follow the steps for multiplying: Factor each expression: u2 – 3u – 10 = (u – 5)(u + 2) and u2 – 10u + 25 = (u – 5)(u – 5) Substitute: u2 – 3u – 10 * u – 5__ = (u – 5)(u + 2) * (u – 5)_ u – 2 u2 – 10u + 25 (u – 2) (u – 5)(u – 5) Cancel: (u – 5)(u + 2) * (u – 5)___ = (u + 2) and this is the final answer. (u – 2) (u – 5)(u – 5) (u – 2) Regents Questions Q1 (Jan 09 Q35) Q2 (Aug 09 Q37) Q3 (June 10 Q37)
Integrated+Algebra+Open+ended+questions.docx