Question

Which statement shows a sum rewritten in the form a ( b + c ) such that the integers b and c have no common factor? Select all that apply. A. 25 + 15 = 5 ( 5 + 3 ) B. 12 + 16 = 9 ( 3 + 7 ) C. 63 + 42 = 7 ( 9 + 6 ) D. 99 + 66 = 33 ( 3 + 2 ) E. 23 + 69 = 23 ( 1 + 3 )

Answer 1

A. 25 + 15 = 5 ( 5 + 3 )

This is ok, because it is a legit factorization and 5 and 3 have no common factor.

B. 12 + 16 = 9 ( 3 + 7 )

This is not ok, because it is not a legit factorization : you can't factor a 9 out of 12 nor 16.

C. 63 + 42 = 7 ( 9 + 6 )

This is not ok. It is a legit factorization , but 9 and 6 have the common factor 3. The complete factorization would be
`21(3+2)`.

D. 99 + 66 = 33 ( 3 + 2 )

This is ok, because it is a legit factorization and 2 and 3 have no common factor.

E. 23 + 69 = 23 ( 1 + 3 )

This is ok, because it is a legit factorization and 1 and 3 have no common factor.

Answer 2

The statement which shows a sum rewritten in the form a ( b + c ) such that the integers b and c have no common factor is:

A. 25 + 15 = 5 ( 5 + 3 )

D. 99 + 66 = 33 ( 3 + 2 )

E. 23 + 69 = 23 ( 1 + 3 )

Explanation:

A.

25 + 15 = 5 ( 5 + 3 )

This is the correct form.

Because greatest common factor of 5 an 3 is: 1

Hence, 5 and 3 have no common factor.

Also,

5 ( 5 + 3 )= 5×5+5×3

i.e.

5 ( 5 + 3 )= 25+15

Hence, option: A is correct.

B.

12 + 16 = 9 ( 3 + 7 )

This property is wrong because.

9 ( 3 + 7 )=9×3+9×7

i.e.

9(3+7)=27+63

Hence, option: B is incorrect.

C.

63 + 42 = 7 ( 9 + 6 )

The expression is correct.

but,

9 and 6 have a common factor as: 3

Hence, option: C is incorrect.

D.

99 + 66 = 33 ( 3 + 2 )

This expression is also correct.

Since,

33(3+2)=33×3+33×2

i.e.

33(3+2)=99+66

Also, 3 an 2 do not have a common factor.

Hence, option: D is correct.

E.

23 + 69 = 23 ( 1 + 3 )

The expression is correct.

since,

23 (1+3)=23×1+23×3

i.e.

23 (1+3)=23+69

Also, 1 and 3 do not have a common factor.

Hence, option: E is correct.