Solve (x^2+2)^2*[5*(x^2+2)^2-3]*(2x)

$$( x ^ { 2 } + 2 ) ^ { 2 } \cdot [ 5 \cdot ( x ^ { 2 } + 2 ) ^ { 2 } - 3 ] \cdot ( 2 x )$$

Evaluate

$$10x\left(x^{2}+2\right)^{4}-6x\left(x^{2}+2\right)^{2}$$

Solution Steps

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

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

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

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

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

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

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

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

Use the distributive property to multiply 5 by x^{4}+4x^{2}+4.

$$\left(x^{4}+4x^{2}+4\right)\left(5x^{4}+20x^{2}+20-3\right)\times 2x$$

Subtract 3 from 20 to get 17.

$$\left(x^{4}+4x^{2}+4\right)\left(5x^{4}+20x^{2}+17\right)\times 2x$$

Use the distributive property to multiply x^{4}+4x^{2}+4 by 5x^{4}+20x^{2}+17 and combine like terms.

$$\left(5x^{8}+40x^{6}+117x^{4}+148x^{2}+68\right)\times 2x$$

Use the distributive property to multiply 5x^{8}+40x^{6}+117x^{4}+148x^{2}+68 by 2.

$$\left(10x^{8}+80x^{6}+234x^{4}+296x^{2}+136\right)x$$

Use the distributive property to multiply 10x^{8}+80x^{6}+234x^{4}+296x^{2}+136 by x.

$$10x^{9}+80x^{7}+234x^{5}+296x^{3}+136x$$

Expand

$$10x^{9}+80x^{7}+234x^{5}+296x^{3}+136x$$

Solution Steps

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

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

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

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

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

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

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

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

Use the distributive property to multiply 5 by x^{4}+4x^{2}+4.

$$\left(x^{4}+4x^{2}+4\right)\left(5x^{4}+20x^{2}+20-3\right)\times 2x$$

Subtract 3 from 20 to get 17.

$$\left(x^{4}+4x^{2}+4\right)\left(5x^{4}+20x^{2}+17\right)\times 2x$$

Use the distributive property to multiply x^{4}+4x^{2}+4 by 5x^{4}+20x^{2}+17 and combine like terms.

$$\left(5x^{8}+40x^{6}+117x^{4}+148x^{2}+68\right)\times 2x$$

Use the distributive property to multiply 5x^{8}+40x^{6}+117x^{4}+148x^{2}+68 by 2.

$$\left(10x^{8}+80x^{6}+234x^{4}+296x^{2}+136\right)x$$

Use the distributive property to multiply 10x^{8}+80x^{6}+234x^{4}+296x^{2}+136 by x.

$$10x^{9}+80x^{7}+234x^{5}+296x^{3}+136x$$