Solve 81w^2z-64x^2z

$$81 w ^ { 2 } z - 64 x ^ { 2 } z$$

Factor

$$z\left(9w-8x\right)\left(8x+9w\right)$$

Solution Steps

Factor out z.

$$z\left(81w^{2}-64x^{2}\right)$$

Consider 81w^{2}-64x^{2}. Rewrite 81w^{2}-64x^{2} as \left(9w\right)^{2}-\left(8x\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(9w-8x\right)\left(9w+8x\right)$$

Reorder the terms.

$$\left(-8x+9w\right)\left(8x+9w\right)$$

Rewrite the complete factored expression.

$$z\left(-8x+9w\right)\left(8x+9w\right)$$

Evaluate

$$z\left(81w^{2}-64x^{2}\right)$$