Solve (2e-f)(3e^2-2ef+f^2)

$$( 2 e - f ) ( 3 e ^ { 2 } - 2 e f + f ^ { 2 } )$$

Evaluate

$$\left(2e-f\right)\left(f^{2}-2ef+3e^{2}\right)$$

Solution Steps

Use the distributive property to multiply 2e-f by 3e^{2}-2ef+f^{2}.

$$2e\left(3e^{2}-2ef\right)+2ef^{2}-f\left(3e^{2}-2ef\right)-f^{3}$$

Use the distributive property to multiply 2e by 3e^{2}-2ef.

$$6e^{3}-4e^{2}f+2ef^{2}-f\left(3e^{2}-2ef\right)-f^{3}$$

Use the distributive property to multiply -f by 3e^{2}-2ef.

$$6e^{3}-4e^{2}f+2ef^{2}-3e^{2}f+2ef^{2}-f^{3}$$

Combine -4e^{2}f and -3e^{2}f to get -7e^{2}f.

$$6e^{3}-7e^{2}f+2ef^{2}+2ef^{2}-f^{3}$$

Combine 2ef^{2} and 2ef^{2} to get 4ef^{2}.

$$6e^{3}-7e^{2}f+4ef^{2}-f^{3}$$

Expand

$$6e^{3}-7e^{2}f+4ef^{2}-f^{3}$$

Solution Steps

Use the distributive property to multiply 2e-f by 3e^{2}-2ef+f^{2}.

$$2e\left(3e^{2}-2ef\right)+2ef^{2}-f\left(3e^{2}-2ef\right)-f^{3}$$

Use the distributive property to multiply 2e by 3e^{2}-2ef.

$$6e^{3}-4e^{2}f+2ef^{2}-f\left(3e^{2}-2ef\right)-f^{3}$$

Use the distributive property to multiply -f by 3e^{2}-2ef.

$$6e^{3}-4e^{2}f+2ef^{2}-3e^{2}f+2ef^{2}-f^{3}$$

Combine -4e^{2}f and -3e^{2}f to get -7e^{2}f.

$$6e^{3}-7e^{2}f+2ef^{2}+2ef^{2}-f^{3}$$

Combine 2ef^{2} and 2ef^{2} to get 4ef^{2}.

$$6e^{3}-7e^{2}f+4ef^{2}-f^{3}$$