Solve 1/8(x+1)(x-5)^2

$$\frac { 1 } { 8 } ( x + 1 ) ( x - 5 ) ^ { 2 }$$

Evaluate

$$\frac{\left(x+1\right)\left(x-5\right)^{2}}{8}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-5\right)^{2}.

$$\frac{1}{8}\left(x+1\right)\left(x^{2}-10x+25\right)$$

Use the distributive property to multiply \frac{1}{8} by x+1.

$$\left(\frac{1}{8}x+\frac{1}{8}\right)\left(x^{2}-10x+25\right)$$

Use the distributive property to multiply \frac{1}{8}x+\frac{1}{8} by x^{2}-10x+25 and combine like terms.

$$\frac{1}{8}x^{3}-\frac{9}{8}x^{2}+\frac{15}{8}x+\frac{25}{8}$$

Expand

$$\frac{x^{3}-9x^{2}+15x+25}{8}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-5\right)^{2}.

$$\frac{1}{8}\left(x+1\right)\left(x^{2}-10x+25\right)$$

Use the distributive property to multiply \frac{1}{8} by x+1.

$$\left(\frac{1}{8}x+\frac{1}{8}\right)\left(x^{2}-10x+25\right)$$

Use the distributive property to multiply \frac{1}{8}x+\frac{1}{8} by x^{2}-10x+25 and combine like terms.

$$\frac{1}{8}x^{3}-\frac{9}{8}x^{2}+\frac{15}{8}x+\frac{25}{8}$$