Solve {c}{4x^2-115x+375}{b^2-400}

$$\left. \begin{array} { c } { 4 x ^ { 2 } - 115 x + 375 } \\ { b ^ { 2 } - 400 } \end{array} \right.$$

Least Common Multiple

$$\left(x-25\right)\left(4x-15\right)\left(b^{2}-400\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$b^{2}-400=\left(b-20\right)\left(b+20\right)$$

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

$$\left(b-20\right)\left(x-25\right)\left(4x-15\right)\left(b+20\right)$$

Expand the expression.

$$4b^{2}x^{2}-1600x^{2}-115xb^{2}+46000x+375b^{2}-150000$$

Evaluate

$$\left(x-25\right)\left(4x-15\right),\ b^{2}-400$$