Solve =w^20.05^2+(1-w)^20.08^2+2w(1-w)*0.3

$$= w ^ { 2 } 0.05 ^ { 2 } + ( 1 - w ) ^ { 2 } 0.08 ^ { 2 } + 2 w ( 1 - w ) \times 0.3$$

Evaluate

$$-\frac{5911w^{2}}{10000}+\frac{367w}{625}+0.0064$$

Solution Steps

Calculate 0.05 to the power of 2 and get 0.0025.

$$w^{2}\times 0.0025+\left(1-w\right)^{2}\times 0.08^{2}+2w\left(1-w\right)\times 0.3$$

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

$$w^{2}\times 0.0025+\left(1-2w+w^{2}\right)\times 0.08^{2}+2w\left(1-w\right)\times 0.3$$

Calculate 0.08 to the power of 2 and get 0.0064.

$$w^{2}\times 0.0025+\left(1-2w+w^{2}\right)\times 0.0064+2w\left(1-w\right)\times 0.3$$

Use the distributive property to multiply 1-2w+w^{2} by 0.0064.

$$w^{2}\times 0.0025+0.0064-0.0128w+0.0064w^{2}+2w\left(1-w\right)\times 0.3$$

Combine w^{2}\times 0.0025 and 0.0064w^{2} to get 0.0089w^{2}.

$$0.0089w^{2}+0.0064-0.0128w+2w\left(1-w\right)\times 0.3$$

Multiply 2 and 0.3 to get 0.6.

$$0.0089w^{2}+0.0064-0.0128w+0.6w\left(1-w\right)$$

Use the distributive property to multiply 0.6w by 1-w.

$$0.0089w^{2}+0.0064-0.0128w+0.6w-0.6w^{2}$$

Combine -0.0128w and 0.6w to get 0.5872w.

$$0.0089w^{2}+0.0064+0.5872w-0.6w^{2}$$

Combine 0.0089w^{2} and -0.6w^{2} to get -0.5911w^{2}.

$$-0.5911w^{2}+0.0064+0.5872w$$

Expand

$$-\frac{5911w^{2}}{10000}+\frac{367w}{625}+0.0064$$

Solution Steps

Calculate 0.05 to the power of 2 and get 0.0025.

$$w^{2}\times 0.0025+\left(1-w\right)^{2}\times 0.08^{2}+2w\left(1-w\right)\times 0.3$$

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

$$w^{2}\times 0.0025+\left(1-2w+w^{2}\right)\times 0.08^{2}+2w\left(1-w\right)\times 0.3$$

Calculate 0.08 to the power of 2 and get 0.0064.

$$w^{2}\times 0.0025+\left(1-2w+w^{2}\right)\times 0.0064+2w\left(1-w\right)\times 0.3$$

Use the distributive property to multiply 1-2w+w^{2} by 0.0064.

$$w^{2}\times 0.0025+0.0064-0.0128w+0.0064w^{2}+2w\left(1-w\right)\times 0.3$$

Combine w^{2}\times 0.0025 and 0.0064w^{2} to get 0.0089w^{2}.

$$0.0089w^{2}+0.0064-0.0128w+2w\left(1-w\right)\times 0.3$$

Multiply 2 and 0.3 to get 0.6.

$$0.0089w^{2}+0.0064-0.0128w+0.6w\left(1-w\right)$$

Use the distributive property to multiply 0.6w by 1-w.

$$0.0089w^{2}+0.0064-0.0128w+0.6w-0.6w^{2}$$

Combine -0.0128w and 0.6w to get 0.5872w.

$$0.0089w^{2}+0.0064+0.5872w-0.6w^{2}$$

Combine 0.0089w^{2} and -0.6w^{2} to get -0.5911w^{2}.

$$-0.5911w^{2}+0.0064+0.5872w$$