Solve 0.5(x+1)^2(x-8)^2

$$0.5 ( x + 1 ) ^ { 2 } ( x - 8 ) ^ { 2 }$$

Evaluate

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

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.

$$0.5\left(x^{2}+2x+1\right)\left(x-8\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-8\right)^{2}.

$$0.5\left(x^{2}+2x+1\right)\left(x^{2}-16x+64\right)$$

Use the distributive property to multiply 0.5 by x^{2}+2x+1.

$$\left(0.5x^{2}+x+0.5\right)\left(x^{2}-16x+64\right)$$

Use the distributive property to multiply 0.5x^{2}+x+0.5 by x^{2}-16x+64 and combine like terms.

$$0.5x^{4}-7x^{3}+16.5x^{2}+56x+32$$

Expand

$$\frac{x^{4}}{2}-7x^{3}+\frac{33x^{2}}{2}+56x+32$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.

$$0.5\left(x^{2}+2x+1\right)\left(x-8\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-8\right)^{2}.

$$0.5\left(x^{2}+2x+1\right)\left(x^{2}-16x+64\right)$$

Use the distributive property to multiply 0.5 by x^{2}+2x+1.

$$\left(0.5x^{2}+x+0.5\right)\left(x^{2}-16x+64\right)$$

Use the distributive property to multiply 0.5x^{2}+x+0.5 by x^{2}-16x+64 and combine like terms.

$$0.5x^{4}-7x^{3}+16.5x^{2}+56x+32$$