Final answer:
To apply the Distributive Property to factor out the GCF, we identify the common factor for all terms and factor it out, like transforming 8x + 12 into 4(2x + 3) where 4 is the GCF.
Step-by-step explanation:
The Distributive Property allows us to multiply a sum by multiplying each addend separately and then adding the products. To use the Distributive Property to factor out the Greatest Common Factor (GCF), we identify the largest factor that is common to all terms in an expression and factor it out. Let's go through each example provided:
- a) 3(5 + 7) = 3×5 + 3×7 = 15 + 21
- b) 2(8 + 9) = 2×8 + 2×9 = 16 + 18
- c) 6(3 + 5) = 6×3 + 6×5 = 18 + 30
- d) 4(6 + 10) = 4×6 + 4×10 = 24 + 40
In all these examples, we multiplied the number outside the parenthesis with each number inside the parenthesis separately. When applying this property to factor out the GCF, you identify common factors in each term and write the expression with the GCF as a factor outside the parentheses.
For instance, to apply the Distributive Property similarly, if we have the expression 8x + 12, the GCF is 4 (since both 8 and 12 are multiples of 4), and factoring it out we get 4(2x + 3).