Solve =w^2005^2+(1-w)^2008^2+2w(1-w)*03*005*008

$$= w ^ { 2 } 005 ^ { 2 } + ( 1 - w ) ^ { 2 } 008 ^ { 2 } + 2 w ( 1 - w ) \times 03 \times 005 \times 008$$

Evaluate

$$\text{Indeterminate}$$

Solution Steps

Multiply 0 and 0 to get 0.

$$w^{2}\times 0\times 5^{2}+\left(1-w\right)^{2}\times 0\times 0\times 8^{2}+2w\left(1-w\right)\times 0\times 3\times 0\times 0\times 5\times 0\times 0\times 8$$

Calculate 5 to the power of 2 and get 25.

$$w^{2}\times 0\times 25+\left(1-w\right)^{2}\times 0\times 0\times 8^{2}+2w\left(1-w\right)\times 0\times 3\times 0\times 0\times 5\times 0\times 0\times 8$$

Multiply 0 and 25 to get 0.

$$w^{2}\times 0+\left(1-w\right)^{2}\times 0\times 0\times 8^{2}+2w\left(1-w\right)\times 0\times 3\times 0\times 0\times 5\times 0\times 0\times 8$$

Anything times zero gives zero.

$$0+\left(1-w\right)^{2}\times 0\times 0\times 8^{2}+2w\left(1-w\right)\times 0\times 3\times 0\times 0\times 5\times 0\times 0\times 8$$

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

$$0+\left(1-2w+w^{2}\right)\times 0\times 0\times 8^{2}+2w\left(1-w\right)\times 0\times 3\times 0\times 0\times 5\times 0\times 0\times 8$$

Multiply 0 and 0 to get 0.

$$0+\left(1-2w+w^{2}\right)\times 0\times 8^{2}+2w\left(1-w\right)\times 0\times 3\times 0\times 0\times 5\times 0\times 0\times 8$$

Calculate 8 to the power of 2 and get 64.

$$0+\left(1-2w+w^{2}\right)\times 0\times 64+2w\left(1-w\right)\times 0\times 3\times 0\times 0\times 5\times 0\times 0\times 8$$

Multiply 0 and 64 to get 0.

$$0+\left(1-2w+w^{2}\right)\times 0+2w\left(1-w\right)\times 0\times 3\times 0\times 0\times 5\times 0\times 0\times 8$$

Anything times zero gives zero.

$$0+0+2w\left(1-w\right)\times 0\times 3\times 0\times 0\times 5\times 0\times 0\times 8$$

Add 0 and 0 to get 0.

$$2w\left(1-w\right)\times 0\times 3\times 0\times 0\times 5\times 0\times 0\times 8$$

Multiply 2 and 0 to get 0.

$$0w\left(1-w\right)\times 3\times 0\times 0\times 5\times 0\times 0\times 8$$

Multiply 0 and 3 to get 0.

$$0w\left(1-w\right)\times 0\times 0\times 5\times 0\times 0\times 8$$

Multiply 0 and 0 to get 0.

$$0w\left(1-w\right)\times 0\times 5\times 0\times 0\times 8$$

Multiply 0 and 0 to get 0.

$$0w\left(1-w\right)\times 5\times 0\times 0\times 8$$

Multiply 0 and 5 to get 0.

$$0w\left(1-w\right)\times 0\times 0\times 8$$

Multiply 0 and 0 to get 0.

$$0w\left(1-w\right)\times 0\times 8$$

Multiply 0 and 0 to get 0.

$$0w\left(1-w\right)\times 8$$

Multiply 0 and 8 to get 0.

$$0w\left(1-w\right)$$

Anything times zero gives zero.

$$0$$