Solve (a-b)^2,(c-a)+(a-c)^2*(a-b)

$$( a - b ) ^ { 2 } , ( c - a ) + ( a - c ) ^ { 2 } \cdot ( a - b )$$

Least Common Multiple

$$\left(a-c\right)\left(a-b\right)^{2}\left(1-bc+ac+ab-a^{2}\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$c-a+\left(a-c\right)^{2}\left(a-b\right)=\left(-a+c\right)\left(-a^{2}+ab+ac-bc+1\right)$$

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

$$\left(a-c\right)\left(a-b\right)^{2}\left(1-bc+ac+ab-a^{2}\right)$$

Expand the expression.

$$-a^{5}+a^{3}+a^{2}b^{3}-3ab^{2}c^{2}+ab^{2}+2abc-2acb^{3}-3b^{2}a^{3}+3ba^{4}+3ba^{2}c^{2}-2ba^{2}-6bca^{3}-c^{2}a^{3}+c^{2}b^{3}+2ca^{4}+6ca^{2}b^{2}-ca^{2}-cb^{2}$$

Evaluate

$$\left(a-b\right)^{2},\left(a-b\right)\left(a-c\right)^{2}+c-a$$