Solve 2(2a^{2}-3b^{2}+4c^{2})+(16^{2}-a^{2}+c^2)+4(a^2-b^2-c^2)

$$2 ( 2 a ^ { 2 } - 3 b ^ { 2 } + 4 c ^ { 2 } ) + ( 16 ^ { 2 } - a ^ { 2 } + c ^ { 2 } ) + 4 ( a ^ { 2 } - b ^ { 2 } - c ^ { 2 } )$$

Evaluate

$$7a^{2}-10b^{2}+5c^{2}+256$$

Solution Steps

Use the distributive property to multiply 2 by 2a^{2}-3b^{2}+4c^{2}.

$$4a^{2}-6b^{2}+8c^{2}+16^{2}-a^{2}+c^{2}+4\left(a^{2}-b^{2}-c^{2}\right)$$

Calculate 16 to the power of 2 and get 256.

$$4a^{2}-6b^{2}+8c^{2}+256-a^{2}+c^{2}+4\left(a^{2}-b^{2}-c^{2}\right)$$

Combine 4a^{2} and -a^{2} to get 3a^{2}.

$$3a^{2}-6b^{2}+8c^{2}+256+c^{2}+4\left(a^{2}-b^{2}-c^{2}\right)$$

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

$$3a^{2}-6b^{2}+9c^{2}+256+4\left(a^{2}-b^{2}-c^{2}\right)$$

Use the distributive property to multiply 4 by a^{2}-b^{2}-c^{2}.

$$3a^{2}-6b^{2}+9c^{2}+256+4a^{2}-4b^{2}-4c^{2}$$

Combine 3a^{2} and 4a^{2} to get 7a^{2}.

$$7a^{2}-6b^{2}+9c^{2}+256-4b^{2}-4c^{2}$$

Combine -6b^{2} and -4b^{2} to get -10b^{2}.

$$7a^{2}-10b^{2}+9c^{2}+256-4c^{2}$$

Combine 9c^{2} and -4c^{2} to get 5c^{2}.

$$7a^{2}-10b^{2}+5c^{2}+256$$

Expand

$$7a^{2}-10b^{2}+5c^{2}+256$$

Solution Steps

Use the distributive property to multiply 2 by 2a^{2}-3b^{2}+4c^{2}.

$$4a^{2}-6b^{2}+8c^{2}+16^{2}-a^{2}+c^{2}+4\left(a^{2}-b^{2}-c^{2}\right)$$

Calculate 16 to the power of 2 and get 256.

$$4a^{2}-6b^{2}+8c^{2}+256-a^{2}+c^{2}+4\left(a^{2}-b^{2}-c^{2}\right)$$

Combine 4a^{2} and -a^{2} to get 3a^{2}.

$$3a^{2}-6b^{2}+8c^{2}+256+c^{2}+4\left(a^{2}-b^{2}-c^{2}\right)$$

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

$$3a^{2}-6b^{2}+9c^{2}+256+4\left(a^{2}-b^{2}-c^{2}\right)$$

Use the distributive property to multiply 4 by a^{2}-b^{2}-c^{2}.

$$3a^{2}-6b^{2}+9c^{2}+256+4a^{2}-4b^{2}-4c^{2}$$

Combine 3a^{2} and 4a^{2} to get 7a^{2}.

$$7a^{2}-6b^{2}+9c^{2}+256-4b^{2}-4c^{2}$$

Combine -6b^{2} and -4b^{2} to get -10b^{2}.

$$7a^{2}-10b^{2}+9c^{2}+256-4c^{2}$$

Combine 9c^{2} and -4c^{2} to get 5c^{2}.

$$7a^{2}-10b^{2}+5c^{2}+256$$