Solve (4a+c)^2-8(2a^2-7ac-c^2)

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

Evaluate

$$c\left(64a+9c\right)$$

Solution Steps

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

$$16a^{2}+8ac+c^{2}-8\left(2a^{2}-7ac-c^{2}\right)$$

Use the distributive property to multiply -8 by 2a^{2}-7ac-c^{2}.

$$16a^{2}+8ac+c^{2}-16a^{2}+56ac+8c^{2}$$

Combine 16a^{2} and -16a^{2} to get 0.

$$8ac+c^{2}+56ac+8c^{2}$$

Combine 8ac and 56ac to get 64ac.

$$64ac+c^{2}+8c^{2}$$

Combine c^{2} and 8c^{2} to get 9c^{2}.

$$64ac+9c^{2}$$

Expand

$$64ac+9c^{2}$$

Solution Steps

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

$$16a^{2}+8ac+c^{2}-8\left(2a^{2}-7ac-c^{2}\right)$$

Use the distributive property to multiply -8 by 2a^{2}-7ac-c^{2}.

$$16a^{2}+8ac+c^{2}-16a^{2}+56ac+8c^{2}$$

Combine 16a^{2} and -16a^{2} to get 0.

$$8ac+c^{2}+56ac+8c^{2}$$

Combine 8ac and 56ac to get 64ac.

$$64ac+c^{2}+8c^{2}$$

Combine c^{2} and 8c^{2} to get 9c^{2}.

$$64ac+9c^{2}$$