Question

Rewrite 11a*22ab using a common factor.

a. 11a(0*2b)
b. 11a(12*b)
c. 11ab(0*2)
d. 11ab(1*22ab)

Answer 1

The expression 11a*22ab is correctly rewritten as 11ab(1*22ab) by factoring out the common term 11a, resulting in 11a*2b or 11a*22b when keeping the factor 11a outside.

Step-by-step explanation:

To rewrite the expression 11a*22ab using a common factor, we can factor out the common terms. In this case, both terms contain the factor 11a. When we take out 11a as a common factor, we get:

11a*22ab = 11a*(2b)*11 = 11a*22b

Therefore, the correct answer is d. 11ab(1*22ab) because 22ab divided by 11a gives us 2b, which we can write as 1*22b to express the common factor out front. Remember, when using the rule of multiplying exponents, which states that (xa)b = xa*b, it simplifies how we combine terms with exponents.

Answer 2

The correct rewrite of 11a*22ab using a common factor is b. 11a(12*b).

Step-by-step explanation:

To rewrite 11a*22ab using a common factor, you first need to identify the greatest common factor (GCF) of the given terms. In this case, the common factor between 11a and 22ab is 11a. To factor out 11a from both terms, divide each term by 11a.

11a*22ab can be expressed as (11a) * (2ab). By simplifying 11a out of 11a*22ab, you're left with 11a multiplied by the remaining term, which is 2ab. Therefore, the correct expression using the common factor is 11a(2ab), which can be further simplified as 11a(12*b) since 2ab equals 12b.

Option b, 11a(12*b), correctly represents the rewritten expression using the greatest common factor 11a and the remaining terms, which are 12 and b. This process is essential in algebraic manipulation to simplify expressions and identify common factors, aiding in further mathematical operations and problem-solving involving polynomials and algebraic equations.