Solve (x^2+a)(x^4-ax^2+a^2

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

Evaluate

$$x^{6}+a^{3}$$

Solution Steps

Use the distributive property to multiply x^{2}+a by x^{4}-ax^{2}+a^{2}.

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

Use the distributive property to multiply x^{2} by x^{4}-ax^{2}.

$$x^{6}-ax^{4}+x^{2}a^{2}+a\left(x^{4}-ax^{2}\right)+a^{3}$$

Use the distributive property to multiply a by x^{4}-ax^{2}.

$$x^{6}-ax^{4}+x^{2}a^{2}+ax^{4}-x^{2}a^{2}+a^{3}$$

Combine -ax^{4} and ax^{4} to get 0.

$$x^{6}+x^{2}a^{2}-x^{2}a^{2}+a^{3}$$

Combine x^{2}a^{2} and -x^{2}a^{2} to get 0.

$$x^{6}+a^{3}$$

Expand

$$x^{6}+a^{3}$$

Solution Steps

Use the distributive property to multiply x^{2}+a by x^{4}-ax^{2}+a^{2}.

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

Use the distributive property to multiply x^{2} by x^{4}-ax^{2}.

$$x^{6}-ax^{4}+x^{2}a^{2}+a\left(x^{4}-ax^{2}\right)+a^{3}$$

Use the distributive property to multiply a by x^{4}-ax^{2}.

$$x^{6}-ax^{4}+x^{2}a^{2}+ax^{4}-x^{2}a^{2}+a^{3}$$

Combine -ax^{4} and ax^{4} to get 0.

$$x^{6}+x^{2}a^{2}-x^{2}a^{2}+a^{3}$$

Combine x^{2}a^{2} and -x^{2}a^{2} to get 0.

$$x^{6}+a^{3}$$