Solve (x^2+9x+20)(x^2-5x+6)(x-5)

$$( x ^ { 2 } + 9 x + 20 ) ( x ^ { 2 } - 5 x + 6 ) ( x - 5 )$$

Evaluate

$$\left(x-3\right)\left(x-2\right)\left(x+4\right)\left(x^{2}-25\right)$$

Solution Steps

Use the distributive property to multiply x^{2}+9x+20 by x^{2}-5x+6 and combine like terms.

$$\left(x^{4}+4x^{3}-19x^{2}-46x+120\right)\left(x-5\right)$$

Use the distributive property to multiply x^{4}+4x^{3}-19x^{2}-46x+120 by x-5 and combine like terms.

$$x^{5}-x^{4}-39x^{3}+49x^{2}+350x-600$$

Expand

$$x^{5}-x^{4}-39x^{3}+49x^{2}+350x-600$$

Solution Steps

Use the distributive property to multiply x^{2}+9x+20 by x^{2}-5x+6 and combine like terms.

$$\left(x^{4}+4x^{3}-19x^{2}-46x+120\right)\left(x-5\right)$$

Use the distributive property to multiply x^{4}+4x^{3}-19x^{2}-46x+120 by x-5 and combine like terms.

$$x^{5}-x^{4}-39x^{3}+49x^{2}+350x-600$$