Solve (x^{2}-4x^2+1)(x^4+3x^2+1)+10x^4

$$( x ^ { 2 } - 4 x ^ { 2 } + 1 ) ( x ^ { 4 } + 3 x ^ { 2 } + 1 ) + 10 x ^ { 4 }$$

Evaluate

$$1+2x^{4}-3x^{6}$$

Solution Steps

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

$$\left(-3x^{2}+1\right)\left(x^{4}+3x^{2}+1\right)+10x^{4}$$

Use the distributive property to multiply -3x^{2}+1 by x^{4}+3x^{2}+1 and combine like terms.

$$-3x^{6}-8x^{4}+1+10x^{4}$$

Combine -8x^{4} and 10x^{4} to get 2x^{4}.

$$-3x^{6}+2x^{4}+1$$

Expand

$$1+2x^{4}-3x^{6}$$

Solution Steps

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

$$\left(-3x^{2}+1\right)\left(x^{4}+3x^{2}+1\right)+10x^{4}$$

Use the distributive property to multiply -3x^{2}+1 by x^{4}+3x^{2}+1 and combine like terms.

$$-3x^{6}-8x^{4}+1+10x^{4}$$

Combine -8x^{4} and 10x^{4} to get 2x^{4}.

$$-3x^{6}+2x^{4}+1$$