Solve left(x-1right)^2+left(3-2xright)^2+left(3x-3right)^2

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

Evaluate

$$14x^{2}-32x+19$$

Solution Steps

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

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

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

$$x^{2}-2x+1+9-12x+4x^{2}+\left(3x-3\right)^{2}$$

Add 1 and 9 to get 10.

$$x^{2}-2x+10-12x+4x^{2}+\left(3x-3\right)^{2}$$

Combine -2x and -12x to get -14x.

$$x^{2}-14x+10+4x^{2}+\left(3x-3\right)^{2}$$

Combine x^{2} and 4x^{2} to get 5x^{2}.

$$5x^{2}-14x+10+\left(3x-3\right)^{2}$$

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

$$5x^{2}-14x+10+9x^{2}-18x+9$$

Combine 5x^{2} and 9x^{2} to get 14x^{2}.

$$14x^{2}-14x+10-18x+9$$

Combine -14x and -18x to get -32x.

$$14x^{2}-32x+10+9$$

Add 10 and 9 to get 19.

$$14x^{2}-32x+19$$

Expand

$$14x^{2}-32x+19$$

Solution Steps

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

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

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

$$x^{2}-2x+1+9-12x+4x^{2}+\left(3x-3\right)^{2}$$

Add 1 and 9 to get 10.

$$x^{2}-2x+10-12x+4x^{2}+\left(3x-3\right)^{2}$$

Combine -2x and -12x to get -14x.

$$x^{2}-14x+10+4x^{2}+\left(3x-3\right)^{2}$$

Combine x^{2} and 4x^{2} to get 5x^{2}.

$$5x^{2}-14x+10+\left(3x-3\right)^{2}$$

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

$$5x^{2}-14x+10+9x^{2}-18x+9$$

Combine 5x^{2} and 9x^{2} to get 14x^{2}.

$$14x^{2}-14x+10-18x+9$$

Combine -14x and -18x to get -32x.

$$14x^{2}-32x+10+9$$

Add 10 and 9 to get 19.

$$14x^{2}-32x+19$$