Solve -0,25*(x+2)^3-1

$$- 0,25 \cdot ( x + 2 ) ^ { 3 } - 1$$

Evaluate

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

Solution Steps

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(x+2\right)^{3}.

$$-0,25\left(x^{3}+6x^{2}+12x+8\right)-1$$

Use the distributive property to multiply -0,25 by x^{3}+6x^{2}+12x+8.

$$-0,25x^{3}-1,5x^{2}-3x-2-1$$

Subtract 1 from -2 to get -3.

$$-0,25x^{3}-1,5x^{2}-3x-3$$

Expand

$$-\frac{x^{3}}{4}-\frac{3x^{2}}{2}-3x-3$$

Solution Steps

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(x+2\right)^{3}.

$$-0,25\left(x^{3}+6x^{2}+12x+8\right)-1$$

Use the distributive property to multiply -0,25 by x^{3}+6x^{2}+12x+8.

$$-0,25x^{3}-1,5x^{2}-3x-2-1$$

Subtract 1 from -2 to get -3.

$$-0,25x^{3}-1,5x^{2}-3x-3$$