Solve {l}{4y^{2}+3x^{2}-2zx^{2}}{5y^{2}+4x^{2}-32x^2}{6y^2+5x^2-4zx^2}

$$\left. \begin{array} { l } { 4 y ^ { 2 } + 3 x ^ { 2 } - 2 z x ^ { 2 } } \\ { 5 y ^ { 2 } + 4 x ^ { 2 } - 32 x ^ { 2 } } \\ { 6 y ^ { 2 } + 5 x ^ { 2 } - 4 z x ^ { 2 } } \end{array} \right.$$

Least Common Multiple

$$\left(5y^{2}-28x^{2}\right)\left(3x^{2}+4y^{2}-2zx^{2}\right)\left(4zx^{2}-6y^{2}-5x^{2}\right)$$

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.

$$\left(5y^{2}-28x^{2}\right)\left(3x^{2}+4y^{2}-2zx^{2}\right)\left(4zx^{2}-6y^{2}-5x^{2}\right)$$

Expand the expression.

$$420x^{6}+482x^{2}y^{4}-120y^{6}+989y^{2}x^{4}-40y^{2}z^{2}x^{4}+224z^{2}x^{6}-616zx^{6}+140zx^{2}y^{4}-674zy^{2}x^{4}$$

Evaluate

$$3x^{2}+4y^{2}-2zx^{2},\ 5y^{2}-28x^{2},\ 5x^{2}+6y^{2}-4zx^{2}$$