Solve 27(3w-8)div9(w-8)(3w-8)

$$27 ( 3 w - 8 ) \div 9 ( w - 8 ) ( 3 w - 8 )$$

Evaluate

$$3\left(w-8\right)\left(3w-8\right)^{2}$$

Solution Steps

Use the distributive property to multiply 27 by 3w-8.

$$\frac{81w-216}{9}\left(w-8\right)\left(3w-8\right)$$

Express \frac{81w-216}{9}\left(w-8\right) as a single fraction.

$$\frac{\left(81w-216\right)\left(w-8\right)}{9}\left(3w-8\right)$$

Express \frac{\left(81w-216\right)\left(w-8\right)}{9}\left(3w-8\right) as a single fraction.

$$\frac{\left(81w-216\right)\left(w-8\right)\left(3w-8\right)}{9}$$

Apply the distributive property by multiplying each term of 81w-216 by each term of w-8.

$$\frac{\left(81w^{2}-648w-216w+1728\right)\left(3w-8\right)}{9}$$

Combine -648w and -216w to get -864w.

$$\frac{\left(81w^{2}-864w+1728\right)\left(3w-8\right)}{9}$$

Apply the distributive property by multiplying each term of 81w^{2}-864w+1728 by each term of 3w-8.

$$\frac{243w^{3}-648w^{2}-2592w^{2}+6912w+5184w-13824}{9}$$

Combine -648w^{2} and -2592w^{2} to get -3240w^{2}.

$$\frac{243w^{3}-3240w^{2}+6912w+5184w-13824}{9}$$

Combine 6912w and 5184w to get 12096w.

$$\frac{243w^{3}-3240w^{2}+12096w-13824}{9}$$

Expand

$$27w^{3}-360w^{2}+1344w-1536$$

Solution Steps

Use the distributive property to multiply 27 by 3w-8.

$$\frac{81w-216}{9}\left(w-8\right)\left(3w-8\right)$$

Express \frac{81w-216}{9}\left(w-8\right) as a single fraction.

$$\frac{\left(81w-216\right)\left(w-8\right)}{9}\left(3w-8\right)$$

Express \frac{\left(81w-216\right)\left(w-8\right)}{9}\left(3w-8\right) as a single fraction.

$$\frac{\left(81w-216\right)\left(w-8\right)\left(3w-8\right)}{9}$$

Apply the distributive property by multiplying each term of 81w-216 by each term of w-8.

$$\frac{\left(81w^{2}-648w-216w+1728\right)\left(3w-8\right)}{9}$$

Combine -648w and -216w to get -864w.

$$\frac{\left(81w^{2}-864w+1728\right)\left(3w-8\right)}{9}$$

Apply the distributive property by multiplying each term of 81w^{2}-864w+1728 by each term of 3w-8.

$$\frac{243w^{3}-648w^{2}-2592w^{2}+6912w+5184w-13824}{9}$$

Combine -648w^{2} and -2592w^{2} to get -3240w^{2}.

$$\frac{243w^{3}-3240w^{2}+6912w+5184w-13824}{9}$$

Combine 6912w and 5184w to get 12096w.

$$\frac{243w^{3}-3240w^{2}+12096w-13824}{9}$$