Factorizing means breaking down an expression into simpler parts (called factors) that when multiplied give the original expression. Let's go through each one step-by-step:
- 6x + 48
Look for the greatest common factor (GCF) of 6x and 48.
- The GCF of 6 and 48 is 6. Both terms have a 6.
Factor out 6:
6x + 48 = 6(x + 8) - 18x² - 3x
Find the GCF of 18x² and 3x.
- The GCF of 18 and 3 is 3.
- Both terms have at least one x.
So, the GCF is 3x.
Factor out 3x:
18x² - 3x = 3x(6x - 1) - 6xy + 10x²y
Find the GCF of 6xy and 10x²y.
- The GCF of 6 and 10 is 2.
- Both terms have x (minimum power x¹) and y.
So, the GCF is 2xy.
Factor out 2xy:
6xy + 10x²y = 2xy(3 + 5x) - P⁴ - 3P²
Find the GCF of P⁴ and 3P².
- The GCF of 1 and 3 is 1.
- Both terms have P with the lowest power P².
So, the GCF is P².
Factor out P²:
P⁴ - 3P² = P²(P² - 3)
Summary:
6x + 48 = 6(x + 8)
18x² - 3x = 3x(6x - 1)
6xy + 10x²y = 2xy(3 + 5x)
P⁴ - 3P² = P²(P² - 3)
If you keep practicing by finding the greatest common factor, factorizing expressions will get easier. Remember to look for common numbers and common letters with the smallest powers!