Solve {l}{(3x-4)(x-4)}{(x+3)(x-7)}{(2x+5)(2x-3)}{(x-9)(2x-3)}{(3-4x)(x-2)}{(5-7x)(1-x)}{(5x-3)(11x+7)}{(11x-7)(11x+7)}{(12-5x)(12+3x)}{(6-3x)(7x-6)}

$$\left. \begin{array} { l } { ( 3 x - 4 ) ( x - 4 ) } \\ { ( x + 3 ) ( x - 7 ) } \\ { ( 2 x + 5 ) ( 2 x - 3 ) } \\ { ( x - 9 ) ( 2 x - 3 ) } \\ { ( 3 - 4 x ) ( x - 2 ) } \\ { ( 5 - 7 x ) ( 1 - x ) } \\ { ( 5 x - 3 ) ( 11 x + 7 ) } \\ { ( 11 x - 7 ) ( 11 x + 7 ) } \\ { ( 12 - 5 x ) ( 12 + 3 x ) } \\ { ( 6 - 3 x ) ( 7 x - 6 ) } \end{array} \right.$$

Least Common Multiple

$$21344400x^{17}-462207900x^{16}[phone]x^{15}[phone]x^{14}-79212168204x^{13}[phone]x^{12}[phone]x^{11}-2546001644010x^{10}[phone]x^{9}[phone]x^{8}-18221162961504x^{7}[phone]x^{6}-18368405597124x^{5}[phone]x^{4}[phone]x^{3}-4772961801216x^{2}[phone]x-172832486400$$

Solution Steps

Factor the expressions that are not already factored.

$$121x^{2}-49=\left(11x-7\right)\left(11x+7\right)$$

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

$$3\left(7114800x^{17}-154069300x^{16}[phone]x^{15}[phone]x^{14}-26404056068x^{13}[phone]x^{12}[phone]x^{11}-848667214670x^{10}[phone]x^{9}[phone]x^{8}-6073720987168x^{7}[phone]x^{6}-6122801865708x^{5}[phone]x^{4}[phone]x^{3}-1590987267072x^{2}[phone]x-57610828800\right)$$

Expand the expression.

$$21344400x^{17}-462207900x^{16}[phone]x^{15}[phone]x^{14}-79212168204x^{13}[phone]x^{12}[phone]x^{11}-2546001644010x^{10}[phone]x^{9}[phone]x^{8}-18221162961504x^{7}[phone]x^{6}-18368405597124x^{5}[phone]x^{4}[phone]x^{3}-4772961801216x^{2}[phone]x-172832486400$$

Evaluate

$$\left(x-4\right)\left(3x-4\right),\ \left(x-7\right)\left(x+3\right),\ \left(2x-3\right)\left(2x+5\right),\ \left(x-9\right)\left(2x-3\right),\ -\left(2-x\right)\left(3-4x\right),\ \left(1-x\right)\left(5-7x\right),\ \left(5x-3\right)\left(11x+7\right),\ 121x^{2}-49,\ 3\left(12-5x\right)\left(x+4\right),\ 3\left(2-x\right)\left(7x-6\right)$$