The first example that comes to mind is that since 12xy is a factor of 36xy, you could use 12xy. This would have the GCF that you want. ■
(x + 5y)(x + 7y)
Rewritten additively.60X2Y + 84XY212XY(5X + 7Y)=============12XY----------greatest gcf
12xy * 3x = 36x2y
6xyz(3x + 2y + z)
4xy
90xy3 = 2 * 32 * 5 * x * y312xy = 22 * 3 * x * yTo find the GCF, you find the highest amounts of each prime factor (2,3,5) and variable (x,y) that are common to both. In this case, one 2, one 3, one x and one y are common.Then multiply these together:2 * 3 * x * y = 6xy
12xy(3y - 4x)
12xy(3y - 4x)
The first example that comes to mind is that since 12xy is a factor of 36xy, you could use 12xy. This would have the GCF that you want. ■
(x + 5y)(x + 7y)
3x x 4y = 12xy
Look for the same variable(s) which have exactly the same exponent(s), group them together, factor out their common variable, then add their coefficients.For example,5x2y3 - 1 - 3x2 + 7y - 10x2y3 - 12xy + 9x2 + 4y + 2= 5x2y3 - 10x2y3 - 3x2 + 9x2 + 7y + 4y - 12xy - 1 + 2= (5 - 10)x2y3 + (-10 - 3)x2 + (7 + 4)y - 12xy + 1= -5x2y3 - 13x2 + 11y - 12xy + 1
Rewritten additively.60X2Y + 84XY212XY(5X + 7Y)=============12XY----------greatest gcf
12xy * 3x = 36x2y
12xy
The only common factor of 10a and 5b is a 5. So the factored form will be something like: 5(2a _ b) assuming the _ is filled in with the proper operation (+ - * / etc.). If the original expression is 10a + 5b, the answer would be 5(2a + b).