Solve 2a(2a-1)^2-(a-2a^2)*(-6a)

$$2 a ( 2 a - 1 ) ^ { 2 } - ( a - 2 a ^ { 2 } ) \cdot ( - 6 a )$$

Evaluate

$$-2a\left(2a-1\right)\left(a+1\right)$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(2a-1\right)^{2}.

$$2a\left(4a^{2}-4a+1\right)-\left(a-2a^{2}\right)\left(-6\right)a$$

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

$$8a^{3}-8a^{2}+2a-\left(a-2a^{2}\right)\left(-6\right)a$$

Use the distributive property to multiply a-2a^{2} by -6.

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

Use the distributive property to multiply -6a+12a^{2} by a.

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

To find the opposite of -6a^{2}+12a^{3}, find the opposite of each term.

$$8a^{3}-8a^{2}+2a+6a^{2}-12a^{3}$$

Combine -8a^{2} and 6a^{2} to get -2a^{2}.

$$8a^{3}-2a^{2}+2a-12a^{3}$$

Combine 8a^{3} and -12a^{3} to get -4a^{3}.

$$-4a^{3}-2a^{2}+2a$$

Expand

$$2a-2a^{2}-4a^{3}$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(2a-1\right)^{2}.

$$2a\left(4a^{2}-4a+1\right)-\left(a-2a^{2}\right)\left(-6\right)a$$

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

$$8a^{3}-8a^{2}+2a-\left(a-2a^{2}\right)\left(-6\right)a$$

Use the distributive property to multiply a-2a^{2} by -6.

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

Use the distributive property to multiply -6a+12a^{2} by a.

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

To find the opposite of -6a^{2}+12a^{3}, find the opposite of each term.

$$8a^{3}-8a^{2}+2a+6a^{2}-12a^{3}$$

Combine -8a^{2} and 6a^{2} to get -2a^{2}.

$$8a^{3}-2a^{2}+2a-12a^{3}$$

Combine 8a^{3} and -12a^{3} to get -4a^{3}.

$$-4a^{3}-2a^{2}+2a$$