Solve 4(w-4)(w-5)(w-2)

$$4 ( w - 4 ) ( w - 5 ) ( w - 2 )$$

Evaluate

$$4\left(w-5\right)\left(w-4\right)\left(w-2\right)$$

Solution Steps

Use the distributive property to multiply 4 by w-4.

$$\left(4w-16\right)\left(w-5\right)\left(w-2\right)$$

Apply the distributive property by multiplying each term of 4w-16 by each term of w-5.

$$\left(4w^{2}-20w-16w+80\right)\left(w-2\right)$$

Combine -20w and -16w to get -36w.

$$\left(4w^{2}-36w+80\right)\left(w-2\right)$$

Apply the distributive property by multiplying each term of 4w^{2}-36w+80 by each term of w-2.

$$4w^{3}-8w^{2}-36w^{2}+72w+80w-160$$

Combine -8w^{2} and -36w^{2} to get -44w^{2}.

$$4w^{3}-44w^{2}+72w+80w-160$$

Combine 72w and 80w to get 152w.

$$4w^{3}-44w^{2}+152w-160$$

Expand

$$4w^{3}-44w^{2}+152w-160$$

Solution Steps

Use the distributive property to multiply 4 by w-4.

$$\left(4w-16\right)\left(w-5\right)\left(w-2\right)$$

Apply the distributive property by multiplying each term of 4w-16 by each term of w-5.

$$\left(4w^{2}-20w-16w+80\right)\left(w-2\right)$$

Combine -20w and -16w to get -36w.

$$\left(4w^{2}-36w+80\right)\left(w-2\right)$$

Apply the distributive property by multiplying each term of 4w^{2}-36w+80 by each term of w-2.

$$4w^{3}-8w^{2}-36w^{2}+72w+80w-160$$

Combine -8w^{2} and -36w^{2} to get -44w^{2}.

$$4w^{3}-44w^{2}+72w+80w-160$$

Combine 72w and 80w to get 152w.

$$4w^{3}-44w^{2}+152w-160$$