Solve left((x+1)(x-3)(x-4)(+x+8)+150right)^2

$${ \left((x+1)(x-3)(x-4)(+x+8)+150 \right) }^{ 2 }$$

Evaluate

$$\left(\left(x-4\right)\left(x-3\right)\left(x+1\right)\left(x+8\right)+150\right)^{2}$$

Solution Steps

Use the distributive property to multiply x+1 by x-3 and combine like terms.

$$\left(\left(x^{2}-2x-3\right)\left(x-4\right)\left(x+8\right)+150\right)^{2}$$

Use the distributive property to multiply x^{2}-2x-3 by x-4 and combine like terms.

$$\left(\left(x^{3}-6x^{2}+5x+12\right)\left(x+8\right)+150\right)^{2}$$

Use the distributive property to multiply x^{3}-6x^{2}+5x+12 by x+8 and combine like terms.

$$\left(x^{4}+2x^{3}-43x^{2}+52x+96+150\right)^{2}$$

Add 96 and 150 to get 246.

$$\left(x^{4}+2x^{3}-43x^{2}+52x+246\right)^{2}$$

Square x^{4}+2x^{3}-43x^{2}+52x+246.

$$x^{8}+4x^{7}-82x^{6}-68x^{5}+2549x^{4}-3488x^{3}-18452x^{2}+25584x+60516$$

Expand

$$x^{8}+4x^{7}-82x^{6}-68x^{5}+2549x^{4}-3488x^{3}-18452x^{2}+25584x+60516$$

Solution Steps

Use the distributive property to multiply x+1 by x-3 and combine like terms.

$$\left(\left(x^{2}-2x-3\right)\left(x-4\right)\left(x+8\right)+150\right)^{2}$$

Use the distributive property to multiply x^{2}-2x-3 by x-4 and combine like terms.

$$\left(\left(x^{3}-6x^{2}+5x+12\right)\left(x+8\right)+150\right)^{2}$$

Use the distributive property to multiply x^{3}-6x^{2}+5x+12 by x+8 and combine like terms.

$$\left(x^{4}+2x^{3}-43x^{2}+52x+96+150\right)^{2}$$

Add 96 and 150 to get 246.

$$\left(x^{4}+2x^{3}-43x^{2}+52x+246\right)^{2}$$

Square x^{4}+2x^{3}-43x^{2}+52x+246.

$$x^{8}+4x^{7}-82x^{6}-68x^{5}+2549x^{4}-3488x^{3}-18452x^{2}+25584x+60516$$