Solve {l}{3a+2b-c,2a+3+c}{ax-ay-az,5ax-7c}

$$\left. \begin{array} { l } { 3 a + 2 b - c , 2 a + 3 + c } \\ { a x - a y - a z , 5 a x - 7 c } \end{array} \right.$$

Least Common Multiple

$$a\left(x-y-z\right)\left(c+2a+3\right)\left(2b+3a-c\right)\left(5ax-7c\right)$$

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.

$$a\left(x-y-z\right)\left(c+2a+3\right)\left(2b+3a-c\right)\left(5ax-7c\right)$$

Expand the expression.

$$10bca^{2}x^{2}+5cx^{2}a^{3}+20bx^{2}a^{3}-5a^{2}c^{2}x^{2}+30x^{2}a^{4}+30ba^{2}x^{2}-15ca^{2}x^{2}+45x^{2}a^{3}+5xya^{2}c^{2}-10bcxya^{2}-20bxya^{3}-5cxya^{3}-30xya^{4}+15cxya^{2}-30bxya^{2}-45xya^{3}+5xza^{2}c^{2}-10bcxza^{2}-20bxza^{3}-5cxza^{3}-30xza^{4}+15cxza^{2}-30bxza^{2}-45xza^{3}-28bcxa^{2}-14abxc^{2}+7axc^{3}-7xa^{2}c^{2}-42cxa^{3}+21axc^{2}-42abcx-63cxa^{2}+14abyc^{2}+28bcya^{2}+7ya^{2}c^{2}+42cya^{3}-7ayc^{3}+42abcy+63cya^{2}-21ayc^{2}+14abzc^{2}+28bcza^{2}+7za^{2}c^{2}+42cza^{3}-7azc^{3}+42abcz+63cza^{2}-21azc^{2}$$

Evaluate

$$2b+3a-c,\ c+2a+3,\ a\left(x-y-z\right),\ 5ax-7c$$