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

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

Evaluate

$$8x^{2}-44x+73$$

Solution Steps

Subtract 2 from -3 to get -5.

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

Subtract 3 from -5 to get -8.

$$\left(2x-8\right)^{2}+\left(2x-3\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-8\right)^{2}.

$$4x^{2}-32x+64+\left(2x-3\right)^{2}$$

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

$$4x^{2}-32x+64+4x^{2}-12x+9$$

Combine 4x^{2} and 4x^{2} to get 8x^{2}.

$$8x^{2}-32x+64-12x+9$$

Combine -32x and -12x to get -44x.

$$8x^{2}-44x+64+9$$

Add 64 and 9 to get 73.

$$8x^{2}-44x+73$$

Expand

$$8x^{2}-44x+73$$

Solution Steps

Subtract 2 from -3 to get -5.

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

Subtract 3 from -5 to get -8.

$$\left(2x-8\right)^{2}+\left(2x-3\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-8\right)^{2}.

$$4x^{2}-32x+64+\left(2x-3\right)^{2}$$

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

$$4x^{2}-32x+64+4x^{2}-12x+9$$

Combine 4x^{2} and 4x^{2} to get 8x^{2}.

$$8x^{2}-32x+64-12x+9$$

Combine -32x and -12x to get -44x.

$$8x^{2}-44x+64+9$$

Add 64 and 9 to get 73.

$$8x^{2}-44x+73$$