Question

Factor 14cd − 28c2d a. 2cd(7 − 14c) b. 2cd(7 − 28c2d) c. 7c2d(2 − 4) d. 7cd(2 − 28c2d)

Answer 1

The expression 14cd − 28
`c^2`d can be factored by taking out the common factor 14cd, resulting in 2cd(7 − 28
`c^2`d).

The correct option is b. 2cd(7 − 28
`c^2`d).

Step-by-step explanation:

The given expression, 14cd − 28c^2d, can be factored by taking out the common factor, which is 14cd. This results in the expression 2cd(7 − 2c). Therefore, the correct factorization is 2cd(7 − 2c). Comparing this with the provided options, the correct choice is option b.

To factor the given expression, start by identifying the common factor of the terms, which is 14cd. Factorizing 14cd out of both terms yields 14cd(1 − 2c). Now, simplify further by recognizing that 1 − 2c can be expressed as −2c + 1. Thus, the final factored form is 2cd(7 − 28
`c^2`d).

Factorization involves breaking down an expression into its constituent factors. In this case, recognizing the common factor and factoring it out simplifies the expression, making it more manageable for further analysis or calculations.

Answer 2

To factor the expression 14cd - 28c^2d, we identify the greatest common factor, which is 7cd, and use it to simplify both terms resulting in the factored form 7cd(2 - 4c).

Step-by-step explanation:

The expression that needs to be factored is 14cd - 28c2d. This is a quadratic equation where both terms have factors in common, specifically 7cd. To factor the expression, we identify the greatest common factor (GCF) and apply it to both terms.

We begin by factoring out the GCF:

1. Identify the GCF of the two terms, which is 7cd.
2. Divide both terms by the GCF: (14cd)/(7cd) = 2 and (28c2d)/(7cd) = 4c.
3. Write the original expression as a product of the GCF and the remaining factors: 7cd(2 - 4c).

Therefore, the factored form of the expression is 7cd(2 - 4c).