Apply the distributive property to factor out the greatest common factor.
[tex]22 c+33 d=[/tex]
Answer (2)
Find the greatest common factor (GCF) of 22 and 33, which is 11.
Express the original expression as 11 × 2 c + 11 × 3 d .
Apply the distributive property to factor out the GCF: 11 ( 2 c + 3 d ) .
The factored expression is 11 ( 2 c + 3 d ) .
Explanation
Understanding the Problem We are asked to factor the expression 22 c + 33 d by applying the distributive property and extracting the greatest common factor (GCF).
Finding the Greatest Common Factor First, we need to find the GCF of the coefficients 22 and 33. We can express 22 as a product of its prime factors: 22 = 2 × 11 . Similarly, we can express 33 as a product of its prime factors: 33 = 3 × 11 .
Identifying the GCF By comparing the prime factorizations of 22 and 33, we identify the common factor as 11. Therefore, the GCF of 22 and 33 is 11.
Applying the Distributive Property Now, we apply the distributive property to factor out the GCF from the expression 22 c + 33 d . We can rewrite the expression as: 22 c + 33 d = 11 × 2 c + 11 × 3 d . Factoring out the 11, we get: 11 ( 2 c + 3 d ) .
Final Answer Thus, the factored form of the expression 22 c + 33 d is 11 ( 2 c + 3 d ) .
Examples
Factoring out the greatest common factor is a useful skill in many real-life situations. For example, suppose you are buying ingredients for a recipe. You need 22 carrots and 33 potatoes. If each carrot and potato costs the same amount, say c dollars for a carrot and d dollars for a potato, then the total cost is 22 c + 33 d . By factoring out the GCF, which is 11, you can rewrite the total cost as 11 ( 2 c + 3 d ) . This means you are essentially buying 11 sets of 2 carrots and 3 potatoes each. This can help you simplify calculations and understand the quantities you are dealing with more easily.
To factor 22 c + 33 d using the distributive property, we first find the greatest common factor, which is 11. We then rewrite the expression as 11 ( 2 c + 3 d ) . The final factored form is 11 ( 2 c + 3 d ) .
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