Solve =P(x)=(x-3)^2(x+1)^2

$$= P ( x ) = ( x - 3 ) ^ { 2 } ( x + 1 ) ^ { 2 }$$

Solve for P

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

$$x\neq 0$$

Steps for Solving Linear Equation

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

$$Px=\left(x^{2}-6x+9\right)\left(x+1\right)^{2}$$

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

$$Px=\left(x^{2}-6x+9\right)\left(x^{2}+2x+1\right)$$

Use the distributive property to multiply x^{2}-6x+9 by x^{2}+2x+1 and combine like terms.

$$Px=x^{4}-4x^{3}-2x^{2}+12x+9$$

The equation is in standard form.

$$xP=x^{4}-4x^{3}-2x^{2}+12x+9$$

Divide both sides by x.

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

Dividing by x undoes the multiplication by x.

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