Solve {l}{[(-x+y)^{2}-(x+y)^{2}][(-x+y)^2+(-x+y)(x+y)+(x+y)^2]+12}{(a-b+3c)(a+b-3c)+(a-b)^2+(a-3c)^2+(6a+2b)(a+c)}

$$\left. \begin{array} { l } { [ ( - x + y ) ^ { 2 } - ( x + y ) ^ { 2 } ] [ ( - x + y ) ^ { 2 } + ( - x + y ) ( x + y ) + ( x + y ) ^ { 2 } ] + 12 } \\ { ( a - b + 3 c ) ( a + b - 3 c ) + ( a - b ) ^ { 2 } + ( a - 3 c ) ^ { 2 } + ( 6 a + 2 b ) ( a + c ) } \end{array} \right.$$

Least Common Multiple

$$96bcxy^{3}+108xa^{2}y^{3}+32bcyx^{3}+36ya^{2}x^{3}-96bc-108a^{2}$$

Solution Steps

Factor the expressions that are not already factored.

$$-12xy^{3}-4yx^{3}+12=4\left(-3xy^{3}-yx^{3}+3\right)$$

Identify all the factors and their highest power in all expressions. Multiply the highest powers of these factors to get the least common multiple.

$$4\left(24bcxy^{3}+27xa^{2}y^{3}+8bcyx^{3}+9ya^{2}x^{3}-24bc-27a^{2}\right)$$

Expand the expression.

$$96bcxy^{3}+108xa^{2}y^{3}+32bcyx^{3}+36ya^{2}x^{3}-96bc-108a^{2}$$

Evaluate

$$12-4yx^{3}-12xy^{3},\ 8bc+9a^{2}$$