Solve 0.5(0.4w^3+0.2w^2)+0.2(0.3w^3-0.4w^2)

$$0.5 ( 0.4 w ^ { 3 } + 0.2 w ^ { 2 } ) + 0.2 ( 0.3 w ^ { 3 } - 0.4 w ^ { 2 } )$$

Evaluate

$$\frac{13w+1}{50}w^{2}$$

Solution Steps

Use the distributive property to multiply 0.5 by 0.4w^{3}+0.2w^{2}.

$$0.2w^{3}+0.1w^{2}+0.2\left(0.3w^{3}-0.4w^{2}\right)$$

Use the distributive property to multiply 0.2 by 0.3w^{3}-0.4w^{2}.

$$0.2w^{3}+0.1w^{2}+0.06w^{3}-0.08w^{2}$$

Combine 0.2w^{3} and 0.06w^{3} to get 0.26w^{3}.

$$0.26w^{3}+0.1w^{2}-0.08w^{2}$$

Combine 0.1w^{2} and -0.08w^{2} to get 0.02w^{2}.

$$0.26w^{3}+0.02w^{2}$$

Expand

$$\frac{13w^{3}+w^{2}}{50}$$

Solution Steps

Use the distributive property to multiply 0.5 by 0.4w^{3}+0.2w^{2}.

$$0.2w^{3}+0.1w^{2}+0.2\left(0.3w^{3}-0.4w^{2}\right)$$

Use the distributive property to multiply 0.2 by 0.3w^{3}-0.4w^{2}.

$$0.2w^{3}+0.1w^{2}+0.06w^{3}-0.08w^{2}$$

Combine 0.2w^{3} and 0.06w^{3} to get 0.26w^{3}.

$$0.26w^{3}+0.1w^{2}-0.08w^{2}$$

Combine 0.1w^{2} and -0.08w^{2} to get 0.02w^{2}.

$$0.26w^{3}+0.02w^{2}$$