12xy * 3x = 36x2y
12y
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. ■
2p = 4y - 12xy - 6x, 3q = 12 - 15y so 2p - 3q = 4y - 12xy - 6x - (12 - 15y) = 4y - 12xy - 6x - 12 + 15y = 19y -12xy - 6x - 12
3x2 - 2y2 = 9x2 + 4y2 - 12xy (subtract 3x2 and add 2y2 to both sides) 0 = 9x2 -3x2 + 4y2 + 2y2 - 12xy 0 = 6x2 + 6y2 - 12xy (divide by 6 to both sides) 0 = x2 + y2 - 12xy or x2 - 2xy + y2 = 0 (x - y)(x - y) = 0 x - y = 0 x = y
3x x 4y = 12xy
12xy * 3x = 36x2y
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
12y
12y
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. ■
2p = 4y - 12xy - 6x, 3q = 12 - 15y so 2p - 3q = 4y - 12xy - 6x - (12 - 15y) = 4y - 12xy - 6x - 12 + 15y = 19y -12xy - 6x - 12
3x2 - 2y2 = 9x2 + 4y2 - 12xy (subtract 3x2 and add 2y2 to both sides) 0 = 9x2 -3x2 + 4y2 + 2y2 - 12xy 0 = 6x2 + 6y2 - 12xy (divide by 6 to both sides) 0 = x2 + y2 - 12xy or x2 - 2xy + y2 = 0 (x - y)(x - y) = 0 x - y = 0 x = y
5
4xy
12xy(3y - 4x)