Solve (x-5)(x-4)left(x-2right)^2

$$(x-5)(x-4) { \left(x-2 \right) }^{ 2 }$$

Expand

$$x^{4}-13x^{3}+60x^{2}-116x+80$$

Solution Steps

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

$$\left(x-5\right)\left(x-4\right)\left(x^{2}-4x+4\right)$$

Use the distributive property to multiply x-5 by x-4 and combine like terms.

$$\left(x^{2}-9x+20\right)\left(x^{2}-4x+4\right)$$

Use the distributive property to multiply x^{2}-9x+20 by x^{2}-4x+4 and combine like terms.

$$x^{4}-13x^{3}+60x^{2}-116x+80$$

Evaluate

$$\left(x-5\right)\left(x-4\right)\left(x-2\right)^{2}$$

Solution Steps

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

$$\left(x-5\right)\left(x-4\right)\left(x^{2}-4x+4\right)$$

Use the distributive property to multiply x-5 by x-4 and combine like terms.

$$\left(x^{2}-9x+20\right)\left(x^{2}-4x+4\right)$$

Use the distributive property to multiply x^{2}-9x+20 by x^{2}-4x+4 and combine like terms.

$$x^{4}-13x^{3}+60x^{2}-116x+80$$