Solve 2/3(x+4)^2-8/3

$$\frac { 2 } { 3 } ( x + 4 ) ^ { 2 } - \frac { 8 } { 3 }$$

Evaluate

$$\frac{2\left(x+2\right)\left(x+6\right)}{3}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+4\right)^{2}.

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

Use the distributive property to multiply \frac{2}{3} by x^{2}+8x+16.

$$\frac{2}{3}x^{2}+\frac{16}{3}x+\frac{32}{3}-\frac{8}{3}$$

Subtract \frac{8}{3} from \frac{32}{3} to get 8.

$$\frac{2}{3}x^{2}+\frac{16}{3}x+8$$

Expand

$$\frac{2x^{2}}{3}+\frac{16x}{3}+8$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+4\right)^{2}.

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

Use the distributive property to multiply \frac{2}{3} by x^{2}+8x+16.

$$\frac{2}{3}x^{2}+\frac{16}{3}x+\frac{32}{3}-\frac{8}{3}$$

Subtract \frac{8}{3} from \frac{32}{3} to get 8.

$$\frac{2}{3}x^{2}+\frac{16}{3}x+8$$