Solve (2y-1)^3-3(2y-1)^2

$$( 2 y - 1 ) ^ { 3 } - 3 ( 2 y - 1 ) ^ { 2 }$$

Evaluate

$$2\left(y-2\right)\left(2y-1\right)^{2}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(2y-1\right)^{3}.

$$8y^{3}-12y^{2}+6y-1-3\left(2y-1\right)^{2}$$

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

$$8y^{3}-12y^{2}+6y-1-3\left(4y^{2}-4y+1\right)$$

Use the distributive property to multiply -3 by 4y^{2}-4y+1.

$$8y^{3}-12y^{2}+6y-1-12y^{2}+12y-3$$

Combine -12y^{2} and -12y^{2} to get -24y^{2}.

$$8y^{3}-24y^{2}+6y-1+12y-3$$

Combine 6y and 12y to get 18y.

$$8y^{3}-24y^{2}+18y-1-3$$

Subtract 3 from -1 to get -4.

$$8y^{3}-24y^{2}+18y-4$$

Expand

$$8y^{3}-24y^{2}+18y-4$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(2y-1\right)^{3}.

$$8y^{3}-12y^{2}+6y-1-3\left(2y-1\right)^{2}$$

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

$$8y^{3}-12y^{2}+6y-1-3\left(4y^{2}-4y+1\right)$$

Use the distributive property to multiply -3 by 4y^{2}-4y+1.

$$8y^{3}-12y^{2}+6y-1-12y^{2}+12y-3$$

Combine -12y^{2} and -12y^{2} to get -24y^{2}.

$$8y^{3}-24y^{2}+6y-1+12y-3$$

Combine 6y and 12y to get 18y.

$$8y^{3}-24y^{2}+18y-1-3$$

Subtract 3 from -1 to get -4.

$$8y^{3}-24y^{2}+18y-4$$