Solve 16(m^2-4)^2-4(3n)^2

$$16 ( m ^ { 2 } - 4 ) ^ { 2 } - 4 ( 3 n ) ^ { 2 }$$

Evaluate

$$4\left(\left(2m^{2}-8\right)^{2}-9n^{2}\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(m^{2}-4\right)^{2}.

$$16\left(\left(m^{2}\right)^{2}-8m^{2}+16\right)-4\times \left(3n\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$16\left(m^{4}-8m^{2}+16\right)-4\times \left(3n\right)^{2}$$

Use the distributive property to multiply 16 by m^{4}-8m^{2}+16.

$$16m^{4}-128m^{2}+256-4\times \left(3n\right)^{2}$$

Expand \left(3n\right)^{2}.

$$16m^{4}-128m^{2}+256-4\times 3^{2}n^{2}$$

Calculate 3 to the power of 2 and get 9.

$$16m^{4}-128m^{2}+256-4\times 9n^{2}$$

Multiply 4 and 9 to get 36.

$$16m^{4}-128m^{2}+256-36n^{2}$$

Expand

$$16m^{4}-128m^{2}-36n^{2}+256$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(m^{2}-4\right)^{2}.

$$16\left(\left(m^{2}\right)^{2}-8m^{2}+16\right)-4\times \left(3n\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$16\left(m^{4}-8m^{2}+16\right)-4\times \left(3n\right)^{2}$$

Use the distributive property to multiply 16 by m^{4}-8m^{2}+16.

$$16m^{4}-128m^{2}+256-4\times \left(3n\right)^{2}$$

Expand \left(3n\right)^{2}.

$$16m^{4}-128m^{2}+256-4\times 3^{2}n^{2}$$

Calculate 3 to the power of 2 and get 9.

$$16m^{4}-128m^{2}+256-4\times 9n^{2}$$

Multiply 4 and 9 to get 36.

$$16m^{4}-128m^{2}+256-36n^{2}$$