Simplify by Factoring
Simplify radical or rational expressions by factoring in Grade 9 Algebra. Pull out perfect square factors or cancel common polynomial factors to reduce expressions.
Key Concepts
Property Always check to see if the numerator of the sum can be factored and if a common factor can be divided out. Explanation Don't stop after adding or subtracting, because your final answer might be wearing a disguise! Always try to factor the final numerator. If you find a factor that matches one in the denominator, you can divide them out to simplify the expression. It’s like cleaning up your work to find the neatest possible answer. Examples $\frac{5x+10}{3(x+2)} = \frac{5(x+2)}{3(x+2)} = \frac{5}{3}$ $\frac{x^2 16}{x^2+x 20} = \frac{(x 4)(x+4)}{(x+5)(x 4)} = \frac{x+4}{x+5}$ $\frac{2x 8}{2x^2 32} = \frac{2(x 4)}{2(x^2 16)} = \frac{2(x 4)}{2(x 4)(x+4)} = \frac{1}{x+4}$.
Common Questions
What is Simplify by Factoring in Grade 9 Algebra?
Property Always check to see if the numerator of the sum can be factored and if a common factor can be divided out Mastering this concept builds a foundation for advanced algebra topics.
How do you approach Simplify by Factoring problems step by step?
Explanation Don't stop after adding or subtracting, because your final answer might be wearing a disguise Use this method consistently to avoid common errors.
What is a common mistake when studying Simplify by Factoring?
If you find a factor that matches one in the denominator, you can divide them out to simplify the expression Always check your work by substituting back into the original problem.