Solve left(x+2right)^3+4x^2=left(x-2right)^3+16

$${ \left(x+2 \right) }^{ 3 } +4 { x }^{ 2 } = { \left(x-2 \right) }^{ 3 } +16$$

Solve for x

$$x=0$$

Steps by Finding Square Root

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

$$x^{3}+6x^{2}+12x+8+4x^{2}=\left(x-2\right)^{3}+16$$

Combine 6x^{2} and 4x^{2} to get 10x^{2}.

$$x^{3}+10x^{2}+12x+8=\left(x-2\right)^{3}+16$$

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

$$x^{3}+10x^{2}+12x+8=x^{3}-6x^{2}+12x-8+16$$

Add -8 and 16 to get 8.

$$x^{3}+10x^{2}+12x+8=x^{3}-6x^{2}+12x+8$$

Subtract x^{3} from both sides.

$$x^{3}+10x^{2}+12x+8-x^{3}=-6x^{2}+12x+8$$

Combine x^{3} and -x^{3} to get 0.

$$10x^{2}+12x+8=-6x^{2}+12x+8$$

Add 6x^{2} to both sides.

$$10x^{2}+12x+8+6x^{2}=12x+8$$

Combine 10x^{2} and 6x^{2} to get 16x^{2}.

$$16x^{2}+12x+8=12x+8$$

Subtract 12x from both sides.

$$16x^{2}+12x+8-12x=8$$

Combine 12x and -12x to get 0.

$$16x^{2}+8=8$$

Subtract 8 from both sides.

$$16x^{2}=8-8$$

Subtract 8 from 8 to get 0.

$$16x^{2}=0$$

Divide both sides by 16. Zero divided by any non-zero number gives zero.

$$x^{2}=0$$

Take the square root of both sides of the equation.

$$x=0 x=0$$

The equation is now solved. Solutions are the same.

$$x=0$$

Steps Using the Quadratic Formula

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

$$x^{3}+6x^{2}+12x+8+4x^{2}=\left(x-2\right)^{3}+16$$

Combine 6x^{2} and 4x^{2} to get 10x^{2}.

$$x^{3}+10x^{2}+12x+8=\left(x-2\right)^{3}+16$$

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

$$x^{3}+10x^{2}+12x+8=x^{3}-6x^{2}+12x-8+16$$

Add -8 and 16 to get 8.

$$x^{3}+10x^{2}+12x+8=x^{3}-6x^{2}+12x+8$$

Subtract x^{3} from both sides.

$$x^{3}+10x^{2}+12x+8-x^{3}=-6x^{2}+12x+8$$

Combine x^{3} and -x^{3} to get 0.

$$10x^{2}+12x+8=-6x^{2}+12x+8$$

Add 6x^{2} to both sides.

$$10x^{2}+12x+8+6x^{2}=12x+8$$

Combine 10x^{2} and 6x^{2} to get 16x^{2}.

$$16x^{2}+12x+8=12x+8$$

Subtract 12x from both sides.

$$16x^{2}+12x+8-12x=8$$

Combine 12x and -12x to get 0.

$$16x^{2}+8=8$$

Subtract 8 from both sides.

$$16x^{2}+8-8=0$$

Subtract 8 from 8 to get 0.

$$16x^{2}=0$$

Divide both sides by 16. Zero divided by any non-zero number gives zero.

$$x^{2}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}}}{2}$$

Take the square root of 0^{2}.

$$x=\frac{0±0}{2}$$

Divide 0 by 2.

$$x=0$$