Solve 1(x-3)^2(x-1)^2

$$1 ( x - 3 ) ^ { 2 } ( x - 1 ) ^ { 2 }$$

Evaluate

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

Solution Steps

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

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

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

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

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

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

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

$$x^{4}-8x^{3}+22x^{2}-24x+9$$

Expand

$$x^{4}-8x^{3}+22x^{2}-24x+9$$

Solution Steps

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

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

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

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

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

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

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

$$x^{4}-8x^{3}+22x^{2}-24x+9$$