Solve (3a-8)^2-(4-7a)^2

$$( 3 a - 8 ) ^ { 2 } - ( 4 - 7 a ) ^ { 2 }$$

Evaluate

$$8\left(6+a-5a^{2}\right)$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(3a-8\right)^{2}.

$$9a^{2}-48a+64-\left(4-7a\right)^{2}$$

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(4-7a\right)^{2}.

$$9a^{2}-48a+64-\left(16-56a+49a^{2}\right)$$

To find the opposite of 16-56a+49a^{2}, find the opposite of each term.

$$9a^{2}-48a+64-16+56a-49a^{2}$$

Subtract 16 from 64 to get 48.

$$9a^{2}-48a+48+56a-49a^{2}$$

Combine -48a and 56a to get 8a.

$$9a^{2}+8a+48-49a^{2}$$

Combine 9a^{2} and -49a^{2} to get -40a^{2}.

$$-40a^{2}+8a+48$$

Expand

$$48+8a-40a^{2}$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(3a-8\right)^{2}.

$$9a^{2}-48a+64-\left(4-7a\right)^{2}$$

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(4-7a\right)^{2}.

$$9a^{2}-48a+64-\left(16-56a+49a^{2}\right)$$

To find the opposite of 16-56a+49a^{2}, find the opposite of each term.

$$9a^{2}-48a+64-16+56a-49a^{2}$$

Subtract 16 from 64 to get 48.

$$9a^{2}-48a+48+56a-49a^{2}$$

Combine -48a and 56a to get 8a.

$$9a^{2}+8a+48-49a^{2}$$

Combine 9a^{2} and -49a^{2} to get -40a^{2}.

$$-40a^{2}+8a+48$$