- Factor polynomial expressions using the Greatest Common Factor (GCF) and by grouping to simplify expressions.
- Factor trinomials and perfect square trinomials into binomials.
- Break down expressions like differences of squares and cubic equations into their simpler factors.
- Use specific methods to factor expressions that contain fractional or negative exponents.
Mastering Advanced Factoring Techniques
Let’s tackle some tricky expressions that really test your factoring skills! Whether you’re dealing with polynomials that have higher degrees, unique coefficients, or require a mix of different factoring tricks, this section is all about leveling up your factoring game and getting you ready to solve real-world problems.
- Perfect Square Trinomials:
[latex]\begin{array}{ccc}\hfill {a}^{2}+2ab+{b}^{2}& =& {\left(a+b\right)}^{2}\hfill \\ & \text{and}& \\ \hfill {a}^{2}-2ab+{b}^{2}& =& {\left(a-b\right)}^{2}\hfill \end{array}[/latex]
- Difference of Squares:
[latex]{a}^{2}-{b}^{2}=\left(a+b\right)\left(a-b\right)[/latex]
- Sum of Two Cubes:
[latex]{a}^{3}+{b}^{3}=\left(a+b\right)\left({a}^{2}-ab+{b}^{2}\right)[/latex]
- Difference of Two Cubes:
[latex]{a}^{3}-{b}^{3}=\left(a-b\right)\left({a}^{2}+ab+{b}^{2}\right)[/latex]