Question 1133672


To find the greatest common factor ({{{GCF}}}) between numbers, take each number and write its prime factorization. Then, identify the factors common to each number and multiply those common factors together. Bam! The {{{GCF}}}!


{{{ 12x^2+16xy+5y^2}}}

={{{ 12x^2+6xy+10xy+5y^2}}}

={{{ (12x^2+6xy)+(10xy+5y^2)}}}

={{{ 6x(2x+y)+5y(2x+y)}}}

={{{(2 x + y) (6 x + 5 y)}}}



{{{30x^2-11xy-30y^2}}}

={{{30x^2-36xy+25xy-30y^2}}}

={{{(30x^2+25xy)-(36xy+30y^2)}}}

={{{5x(6x+5y)-6y(6x+5y)}}}

 ={{{(6 x + 5 y) (5 x - 6 y)}}}



{{{ 6x^2-xy-5y^2}}}

={{{ 6x^2-6xy+5xy-5y^2}}}

={{{ (6x^2-6xy)+(5xy-5y^2)}}}

={{{ 6x(x-y)+5y(x-y)}}}

 ={{{(6 x + 5 y) (x - y)}}}


=>The {{{GCF}}} is {{{(6 x + 5 y)}}}