Solve (a-b)(a+b)(a^4+a^2b^2+b^4)

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

Evaluate

$$\left(a^{2}-b^{2}\right)\left(-\left(ab\right)^{2}+\left(a^{2}+b^{2}\right)^{2}\right)$$

Solution Steps

Use the distributive property to multiply a-b by a+b and combine like terms.

$$\left(a^{2}-b^{2}\right)\left(a^{4}+a^{2}b^{2}+b^{4}\right)$$

Use the distributive property to multiply a^{2}-b^{2} by a^{4}+a^{2}b^{2}+b^{4} and combine like terms.

$$a^{6}-b^{6}$$

Expand

$$a^{6}-b^{6}$$

Solution Steps

Use the distributive property to multiply a-b by a+b and combine like terms.

$$\left(a^{2}-b^{2}\right)\left(a^{4}+a^{2}b^{2}+b^{4}\right)$$

Use the distributive property to multiply a^{2}-b^{2} by a^{4}+a^{2}b^{2}+b^{4} and combine like terms.

$$a^{6}-b^{6}$$