Solve {l}{(5y^{2}-3xy+x^{2})-(7y^{2}-9xy+x^{2})}{(4a^{2}-5ab^{2}-10a^2b)+(4ab^2+17a^2b-6a^2)}

$$\left. \begin{array} { l } { ( 5 y ^ { 2 } - 3 x y + x ^ { 2 } ) - ( 7 y ^ { 2 } - 9 x y + x ^ { 2 } ) } \\ { ( 4 a ^ { 2 } - 5 a b ^ { 2 } - 10 a ^ { 2 } b ) + ( 4 a b ^ { 2 } + 17 a ^ { 2 } b - 6 a ^ { 2 } ) } \end{array} \right.$$

Least Common Multiple

$$2ay\left(y-3x\right)\left(7ab-b^{2}-2a\right)$$

Solution Steps

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

$$2ay\left(y-3x\right)\left(7ab-b^{2}-2a\right)$$

Expand the expression.

$$6axyb^{2}-42bxya^{2}+12xya^{2}+14ba^{2}y^{2}-2ab^{2}y^{2}-4a^{2}y^{2}$$

Evaluate

$$2y\left(3x-y\right),\ a\left(7ab-b^{2}-2a\right)$$