Factor the expression below completely, if possible 18 m 3 n − 57 m 2 n 2 + 42 m n 3 18 m ^ { 3 } n - 57 m ^ { 2 } n ^ { 2 } + 42 m n ^ { 3 } 18 m 3 n − 57 m 2 n 2 + 42 m n 3 A) 3 m n ( m − 2 n ) ( 6 m − 7 n ) 3 m n ( m - 2 n ) ( 6 m - 7 n ) 3 mn ( m − 2 n ) ( 6 m − 7 n ) B) 3 m n ( m + 2 n ) ( 6 m + 7 n ) 3 m n ( m + 2 n ) ( 6 m + 7 n ) 3 mn ( m + 2 n ) ( 6 m + 7 n ) C) 3 m n ( m − 2 n ) ( 6 m + 7 n ) 3 m n ( m - 2 n ) ( 6 m + 7 n ) 3 mn ( m − 2 n ) ( 6 m + 7 n ) D) 3 m n ( m + 2 n ) ( 6 m − 7 n ) 3 m n ( m + 2 n ) ( 6 m - 7 n ) 3 mn ( m + 2 n ) ( 6 m − 7 n ) E) The expression is prime.

Question

Factor the expression below completely, if possible   18 m 3 n − 57 m 2 n 2 + 42 m n 3 18 m ^ { 3 } n - 57 m ^ { 2 } n ^ { 2 } + 42 m n ^ { 3 } 18 m 3 n − 57 m 2 n 2 + 42 m n 3 A)    3 m n ( m − 2 n )  ( 6 m − 7 n )  3 m n ( m - 2 n )  ( 6 m - 7 n )  3 mn ( m − 2 n )  ( 6 m − 7 n )  B)    3 m n ( m + 2 n )  ( 6 m + 7 n )  3 m n ( m + 2 n )  ( 6 m + 7 n )  3 mn ( m + 2 n )  ( 6 m + 7 n )  C)    3 m n ( m − 2 n )  ( 6 m + 7 n )  3 m n ( m - 2 n )  ( 6 m + 7 n )  3 mn ( m − 2 n )  ( 6 m + 7 n )  D)    3 m n ( m + 2 n )  ( 6 m − 7 n )  3 m n ( m + 2 n )  ( 6 m - 7 n )  3 mn ( m + 2 n )  ( 6 m − 7 n )  E) The expression is prime.

María Camila · Accepted Answer

Final Answer : A, Explanation :   First, factor out the greatest common factor, which is   3 m n 3mn 3 mn  , resulting in   3 m n ( 6 m 2 − 19 m n + 14 n 2 ) 3mn(6m^2 - 19mn + 14n^2) 3 mn ( 6 m 2 − 19 mn + 14 n 2 )  . Factoring the trinomial inside the parentheses gives   3 m n ( m − 2 n ) ( 6 m − 7 n ) 3mn(m-2n)(6m-7n) 3 mn ( m − 2 n ) ( 6 m − 7 n )  .

Factor the expression below completely, if possible $18 m ^ { 3 } n - 57 m ^ { 2 } n ^ { 2 } + 42 m n ^ { 3 }$

A) $3 mn (m - 2 n) (6 m - 7 n)$
B) $3 mn (m + 2 n) (6 m + 7 n)$
C) $3 mn (m - 2 n) (6 m + 7 n)$
D) $3 mn (m + 2 n) (6 m - 7 n)$
E) The expression is prime.

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