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 .
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
12xy
In case you meant 64x^3 - 27y^3, that factors to (4x - 3y)(16x^2 + 12xy + 9y^2)
(4x - 3y)(16x^2 + 12xy + 9y^2)
The expressions (4xy - 9xy) and (12xy) are called terms because they each represent a single mathematical entity within an algebraic expression. Terms can consist of constants, variables, or the product of constants and variables. In this case, (4xy), (-9xy), and (12xy) are all terms that involve the variable (xy) multiplied by coefficients. When combined, they can be simplified and manipulated in algebraic operations.
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