Solve {l}{(3x+5)+(5x+3)}{(7-8y^{3})+(4-y^{3}-v)}{(7x-x^{3}+5x^{2})+(2x^{2}+5x^{3})}{(n^2-5n+7n^3)+(6+6n^2-5n^3)}

$$\left. \begin{array} { l } { ( 3 x + 5 ) + ( 5 x + 3 ) } \\ { ( 7 - 8 y ^ { 3 } ) + ( 4 - y ^ { 3 } - v ) } \\ { ( 7 x - x ^ { 3 } + 5 x ^ { 2 } ) + ( 2 x ^ { 2 } + 5 x ^ { 3 } ) } \\ { ( n ^ { 2 } - 5 n + 7 n ^ { 3 } ) + ( 6 + 6 n ^ { 2 } - 5 n ^ { 3 } ) } \end{array} \right.$$

Least Common Multiple

$$8x\left(x+1\right)\left(9y^{3}+v-11\right)\left(8x^{2}n^{3}-20nx^{2}+24x^{2}+14xn^{3}+49xn^{2}-35nx+42x+28\left(nx\right)^{2}+14n^{3}+49n^{2}-35n+42\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$8+8x=8\left(x+1\right)$$

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

$$8x\left(x+1\right)\left(9y^{3}+v-11\right)\left(8x^{2}n^{3}+28n^{2}x^{2}-20nx^{2}+24x^{2}+14xn^{3}+49xn^{2}-35nx+42x+14n^{3}+49n^{2}-35n+42\right)$$

Expand the expression.

$$64vn^{3}x^{4}+224vn^{2}x^{4}-704n^{3}x^{4}-160nvx^{4}-2464n^{2}x^{4}+192vx^{4}+1760nx^{4}-2112x^{4}+1584n^{3}x^{3}y^{3}+5544n^{2}x^{3}y^{3}+176vn^{3}x^{3}-3960nx^{3}y^{3}+616vn^{2}x^{3}+4752x^{3}y^{3}-1936n^{3}x^{3}-440nvx^{3}-6776n^{2}x^{3}+528vx^{3}+4840nx^{3}-5808x^{3}+2016x^{2}n^{3}y^{3}+7056n^{2}x^{2}y^{3}-5040nx^{2}y^{3}+6048x^{2}y^{3}+224vx^{2}n^{3}+784vn^{2}x^{2}-2464x^{2}n^{3}-560nvx^{2}-8624n^{2}x^{2}+672vx^{2}+6160nx^{2}-7392x^{2}+1008xn^{3}y^{3}+3528xn^{2}y^{3}-2520nxy^{3}+3024xy^{3}+112vxn^{3}+392vxn^{2}-1232xn^{3}-280nvx-4312xn^{2}+336vx+3080nx-3696x+576n^{3}y^{3}x^{4}+2016n^{2}y^{3}x^{4}-1440ny^{3}x^{4}+1728y^{3}x^{4}$$

Evaluate

$$8\left(x+1\right),\ 11-v-9y^{3},\ x\left(4x^{2}+7x+7\right),\ 2n^{3}+7n^{2}-5n+6$$