Solve {l}{(3a+7b)(3a-7)}{(x^2-1)(x^2+1)}

$$\left. \begin{array} { l } { ( 3 a + 7 b ) ( 3 a - 7 ) } \\ { ( x ^ { 2 } - 1 ) ( x ^ { 2 } + 1 ) } \end{array} \right.$$

Least Common Multiple

$$\left(3a-7\right)\left(3a+7b\right)\left(x^{4}-1\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$9a^{2}-21a+21ba-49b=\left(3a-7\right)\left(3a+7b\right) x^{4}-1=\left(x-1\right)\left(x+1\right)\left(x^{2}+1\right)$$

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

$$\left(x-1\right)\left(3a-7\right)\left(x+1\right)\left(3a+7b\right)\left(x^{2}+1\right)$$

Expand the expression.

$$21abx^{4}+9a^{2}x^{4}-49bx^{4}-21ax^{4}-21ab-9a^{2}+21a+49b$$

Evaluate

$$\left(3a-7\right)\left(3a+7b\right),\ x^{4}-1$$