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

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

Evaluate

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

Solution Steps

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

$$\left(\left(x^{2}\right)^{2}+6x^{2}+9\right)\left(x^{2}-2x+4\right)$$

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

$$\left(x^{4}+6x^{2}+9\right)\left(x^{2}-2x+4\right)$$

Use the distributive property to multiply x^{4}+6x^{2}+9 by x^{2}-2x+4 and combine like terms.

$$x^{6}-2x^{5}+10x^{4}-12x^{3}+33x^{2}-18x+36$$

Expand

$$x^{6}-2x^{5}+10x^{4}-12x^{3}+33x^{2}-18x+36$$

Solution Steps

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

$$\left(\left(x^{2}\right)^{2}+6x^{2}+9\right)\left(x^{2}-2x+4\right)$$

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

$$\left(x^{4}+6x^{2}+9\right)\left(x^{2}-2x+4\right)$$

Use the distributive property to multiply x^{4}+6x^{2}+9 by x^{2}-2x+4 and combine like terms.

$$x^{6}-2x^{5}+10x^{4}-12x^{3}+33x^{2}-18x+36$$