Solve =(5x^2+2)(x^2-4)^3

$$= ( 5 x ^ { 2 } + 2 ) ( x ^ { 2 } - 4 ) ^ { 3 }$$

Evaluate

$$\left(5x^{2}+2\right)\left(x^{2}-4\right)^{3}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x^{2}-4\right)^{3}.

$$\left(5x^{2}+2\right)\left(\left(x^{2}\right)^{3}-12\left(x^{2}\right)^{2}+48x^{2}-64\right)$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\left(5x^{2}+2\right)\left(x^{6}-12\left(x^{2}\right)^{2}+48x^{2}-64\right)$$

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

$$\left(5x^{2}+2\right)\left(x^{6}-12x^{4}+48x^{2}-64\right)$$

Use the distributive property to multiply 5x^{2}+2 by x^{6}-12x^{4}+48x^{2}-64 and combine like terms.

$$5x^{8}-58x^{6}+216x^{4}-224x^{2}-128$$

Expand

$$5x^{8}-58x^{6}+216x^{4}-224x^{2}-128$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x^{2}-4\right)^{3}.

$$\left(5x^{2}+2\right)\left(\left(x^{2}\right)^{3}-12\left(x^{2}\right)^{2}+48x^{2}-64\right)$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\left(5x^{2}+2\right)\left(x^{6}-12\left(x^{2}\right)^{2}+48x^{2}-64\right)$$

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

$$\left(5x^{2}+2\right)\left(x^{6}-12x^{4}+48x^{2}-64\right)$$

Use the distributive property to multiply 5x^{2}+2 by x^{6}-12x^{4}+48x^{2}-64 and combine like terms.

$$5x^{8}-58x^{6}+216x^{4}-224x^{2}-128$$