Solve 8a^6b^4c^6-2d^2

$$8 a ^ { 6 } b ^ { 4 } c ^ { 6 } - 2 d ^ { 2 }$$

Factor

$$2\left(2b^{2}a^{3}c^{3}-d\right)\left(2b^{2}a^{3}c^{3}+d\right)$$

Solution Steps

Factor out 2.

$$2\left(4a^{6}b^{4}c^{6}-d^{2}\right)$$

Consider 4a^{6}b^{4}c^{6}-d^{2}. Rewrite 4a^{6}b^{4}c^{6}-d^{2} as \left(2a^{3}b^{2}c^{3}\right)^{2}-d^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

$$\left(2a^{3}b^{2}c^{3}-d\right)\left(2a^{3}b^{2}c^{3}+d\right)$$

Reorder the terms.

$$\left(2b^{2}a^{3}c^{3}-d\right)\left(2b^{2}a^{3}c^{3}+d\right)$$

Rewrite the complete factored expression.

$$2\left(2b^{2}a^{3}c^{3}-d\right)\left(2b^{2}a^{3}c^{3}+d\right)$$

Evaluate

$$8b^{4}\left(ac\right)^{6}-2d^{2}$$