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

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

Evaluate

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

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3x+1\right)^{2}.

$$9x^{2}+6x+1+\left(2x-3\right)^{2}+\left(2-x\right)^{2}$$

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

$$9x^{2}+6x+1+4x^{2}-12x+9+\left(2-x\right)^{2}$$

Combine 9x^{2} and 4x^{2} to get 13x^{2}.

$$13x^{2}+6x+1-12x+9+\left(2-x\right)^{2}$$

Combine 6x and -12x to get -6x.

$$13x^{2}-6x+1+9+\left(2-x\right)^{2}$$

Add 1 and 9 to get 10.

$$13x^{2}-6x+10+\left(2-x\right)^{2}$$

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

$$13x^{2}-6x+10+4-4x+x^{2}$$

Add 10 and 4 to get 14.

$$13x^{2}-6x+14-4x+x^{2}$$

Combine -6x and -4x to get -10x.

$$13x^{2}-10x+14+x^{2}$$

Combine 13x^{2} and x^{2} to get 14x^{2}.

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

Expand

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

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3x+1\right)^{2}.

$$9x^{2}+6x+1+\left(2x-3\right)^{2}+\left(2-x\right)^{2}$$

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

$$9x^{2}+6x+1+4x^{2}-12x+9+\left(2-x\right)^{2}$$

Combine 9x^{2} and 4x^{2} to get 13x^{2}.

$$13x^{2}+6x+1-12x+9+\left(2-x\right)^{2}$$

Combine 6x and -12x to get -6x.

$$13x^{2}-6x+1+9+\left(2-x\right)^{2}$$

Add 1 and 9 to get 10.

$$13x^{2}-6x+10+\left(2-x\right)^{2}$$

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

$$13x^{2}-6x+10+4-4x+x^{2}$$

Add 10 and 4 to get 14.

$$13x^{2}-6x+14-4x+x^{2}$$

Combine -6x and -4x to get -10x.

$$13x^{2}-10x+14+x^{2}$$

Combine 13x^{2} and x^{2} to get 14x^{2}.

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