To square a number or an entire segment with variables, parenthesize the particular section and write a square power outside. In this case, it is (12xy)^2. In expanded form, it is 144 . x^2 . y^2 .
2 * 2 * 3 * x * y * y
4xy
12xy(3y - 4x)
The GCF is 3x.
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
33
3x x 4y = 12xy
12xy * 3x = 36x2y
In case you meant 64x^3 - 27y^3, that factors to (4x - 3y)(16x^2 + 12xy + 9y^2)
12xy
(4x - 3y)(16x^2 + 12xy + 9y^2)
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