Solve (8a-1)^2-(3a-1)(2a+1)

$$( 8 a - 1 ) ^ { 2 } - ( 3 a - 1 ) ( 2 a + 1 )$$

Evaluate

$$58a^{2}-17a+2$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(8a-1\right)^{2}.

$$64a^{2}-16a+1-\left(3a-1\right)\left(2a+1\right)$$

Use the distributive property to multiply 3a-1 by 2a+1 and combine like terms.

$$64a^{2}-16a+1-\left(6a^{2}+a-1\right)$$

To find the opposite of 6a^{2}+a-1, find the opposite of each term.

$$64a^{2}-16a+1-6a^{2}-a+1$$

Combine 64a^{2} and -6a^{2} to get 58a^{2}.

$$58a^{2}-16a+1-a+1$$

Combine -16a and -a to get -17a.

$$58a^{2}-17a+1+1$$

Add 1 and 1 to get 2.

$$58a^{2}-17a+2$$

Expand

$$58a^{2}-17a+2$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(8a-1\right)^{2}.

$$64a^{2}-16a+1-\left(3a-1\right)\left(2a+1\right)$$

Use the distributive property to multiply 3a-1 by 2a+1 and combine like terms.

$$64a^{2}-16a+1-\left(6a^{2}+a-1\right)$$

To find the opposite of 6a^{2}+a-1, find the opposite of each term.

$$64a^{2}-16a+1-6a^{2}-a+1$$

Combine 64a^{2} and -6a^{2} to get 58a^{2}.

$$58a^{2}-16a+1-a+1$$

Combine -16a and -a to get -17a.

$$58a^{2}-17a+1+1$$

Add 1 and 1 to get 2.

$$58a^{2}-17a+2$$