Solve (2a-1)(a-7)(+6a-3)(2a-1)

$$( 2 a - 1 ) ( a - 7 ) ( + 6 a - 3 ) ( 2 a - 1 )$$

Evaluate

$$3\left(a-7\right)\left(2a-1\right)^{3}$$

Solution Steps

Multiply 2a-1 and 2a-1 to get \left(2a-1\right)^{2}.

$$\left(2a-1\right)^{2}\left(a-7\right)\left(6a-3\right)$$

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

$$\left(4a^{2}-4a+1\right)\left(a-7\right)\left(6a-3\right)$$

Apply the distributive property by multiplying each term of 4a^{2}-4a+1 by each term of a-7.

$$\left(4a^{3}-28a^{2}-4a^{2}+28a+a-7\right)\left(6a-3\right)$$

Combine -28a^{2} and -4a^{2} to get -32a^{2}.

$$\left(4a^{3}-32a^{2}+28a+a-7\right)\left(6a-3\right)$$

Combine 28a and a to get 29a.

$$\left(4a^{3}-32a^{2}+29a-7\right)\left(6a-3\right)$$

Apply the distributive property by multiplying each term of 4a^{3}-32a^{2}+29a-7 by each term of 6a-3.

$$24a^{4}-12a^{3}-192a^{3}+96a^{2}+174a^{2}-87a-42a+21$$

Combine -12a^{3} and -192a^{3} to get -204a^{3}.

$$24a^{4}-204a^{3}+96a^{2}+174a^{2}-87a-42a+21$$

Combine 96a^{2} and 174a^{2} to get 270a^{2}.

$$24a^{4}-204a^{3}+270a^{2}-87a-42a+21$$

Combine -87a and -42a to get -129a.

$$24a^{4}-204a^{3}+270a^{2}-129a+21$$

Expand

$$24a^{4}-204a^{3}+270a^{2}-129a+21$$

Solution Steps

Multiply 2a-1 and 2a-1 to get \left(2a-1\right)^{2}.

$$\left(2a-1\right)^{2}\left(a-7\right)\left(6a-3\right)$$

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

$$\left(4a^{2}-4a+1\right)\left(a-7\right)\left(6a-3\right)$$

Apply the distributive property by multiplying each term of 4a^{2}-4a+1 by each term of a-7.

$$\left(4a^{3}-28a^{2}-4a^{2}+28a+a-7\right)\left(6a-3\right)$$

Combine -28a^{2} and -4a^{2} to get -32a^{2}.

$$\left(4a^{3}-32a^{2}+28a+a-7\right)\left(6a-3\right)$$

Combine 28a and a to get 29a.

$$\left(4a^{3}-32a^{2}+29a-7\right)\left(6a-3\right)$$

Apply the distributive property by multiplying each term of 4a^{3}-32a^{2}+29a-7 by each term of 6a-3.

$$24a^{4}-12a^{3}-192a^{3}+96a^{2}+174a^{2}-87a-42a+21$$

Combine -12a^{3} and -192a^{3} to get -204a^{3}.

$$24a^{4}-204a^{3}+96a^{2}+174a^{2}-87a-42a+21$$

Combine 96a^{2} and 174a^{2} to get 270a^{2}.

$$24a^{4}-204a^{3}+270a^{2}-87a-42a+21$$

Combine -87a and -42a to get -129a.

$$24a^{4}-204a^{3}+270a^{2}-129a+21$$