Solve varphi+(p-3)+(p-3)^2+2/3(p-3)

$$\varphi + ( p - 3 ) + ( p - 3 ) ^ { 2 } + \frac { 2 } { 3 } ( p - 3 )$$

Evaluate

$$p^{2}-\frac{13p}{3}+\phi +4$$

Solution Steps

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

$$\phi +p-3+p^{2}-6p+9+\frac{2}{3}\left(p-3\right)$$

Combine p and -6p to get -5p.

$$\phi -5p-3+p^{2}+9+\frac{2}{3}\left(p-3\right)$$

Add -3 and 9 to get 6.

$$\phi -5p+6+p^{2}+\frac{2}{3}\left(p-3\right)$$

Use the distributive property to multiply \frac{2}{3} by p-3.

$$\phi -5p+6+p^{2}+\frac{2}{3}p-2$$

Combine -5p and \frac{2}{3}p to get -\frac{13}{3}p.

$$\phi -\frac{13}{3}p+6+p^{2}-2$$

Subtract 2 from 6 to get 4.

$$\phi -\frac{13}{3}p+4+p^{2}$$

Expand

$$p^{2}-\frac{13p}{3}+\phi +4$$

Solution Steps

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

$$\phi +p-3+p^{2}-6p+9+\frac{2}{3}\left(p-3\right)$$

Combine p and -6p to get -5p.

$$\phi -5p-3+p^{2}+9+\frac{2}{3}\left(p-3\right)$$

Add -3 and 9 to get 6.

$$\phi -5p+6+p^{2}+\frac{2}{3}\left(p-3\right)$$

Use the distributive property to multiply \frac{2}{3} by p-3.

$$\phi -5p+6+p^{2}+\frac{2}{3}p-2$$

Combine -5p and \frac{2}{3}p to get -\frac{13}{3}p.

$$\phi -\frac{13}{3}p+6+p^{2}-2$$

Subtract 2 from 6 to get 4.

$$\phi -\frac{13}{3}p+4+p^{2}$$