Solve -9(3b+6)(2b)(3b-8)(3b+8)

$$- 9 ( 3 b + 6 ) ( 2 b ) ( 3 b - 8 ) ( 3 b + 8 )$$

Evaluate

$$-54b\left(b+2\right)\left(9b^{2}-64\right)$$

Solution Steps

Multiply -9 and 2 to get -18.

$$-18\left(3b+6\right)b\left(3b-8\right)\left(3b+8\right)$$

Use the distributive property to multiply -18 by 3b+6.

$$\left(-54b-108\right)b\left(3b-8\right)\left(3b+8\right)$$

Use the distributive property to multiply -54b-108 by b.

$$\left(-54b^{2}-108b\right)\left(3b-8\right)\left(3b+8\right)$$

Apply the distributive property by multiplying each term of -54b^{2}-108b by each term of 3b-8.

$$\left(-162b^{3}+432b^{2}-324b^{2}+864b\right)\left(3b+8\right)$$

Combine 432b^{2} and -324b^{2} to get 108b^{2}.

$$\left(-162b^{3}+108b^{2}+864b\right)\left(3b+8\right)$$

Apply the distributive property by multiplying each term of -162b^{3}+108b^{2}+864b by each term of 3b+8.

$$-486b^{4}-1296b^{3}+324b^{3}+864b^{2}+2592b^{2}+6912b$$

Combine -1296b^{3} and 324b^{3} to get -972b^{3}.

$$-486b^{4}-972b^{3}+864b^{2}+2592b^{2}+6912b$$

Combine 864b^{2} and 2592b^{2} to get 3456b^{2}.

$$-486b^{4}-972b^{3}+3456b^{2}+6912b$$

Expand

$$6912b+3456b^{2}-972b^{3}-486b^{4}$$

Solution Steps

Multiply -9 and 2 to get -18.

$$-18\left(3b+6\right)b\left(3b-8\right)\left(3b+8\right)$$

Use the distributive property to multiply -18 by 3b+6.

$$\left(-54b-108\right)b\left(3b-8\right)\left(3b+8\right)$$

Use the distributive property to multiply -54b-108 by b.

$$\left(-54b^{2}-108b\right)\left(3b-8\right)\left(3b+8\right)$$

Apply the distributive property by multiplying each term of -54b^{2}-108b by each term of 3b-8.

$$\left(-162b^{3}+432b^{2}-324b^{2}+864b\right)\left(3b+8\right)$$

Combine 432b^{2} and -324b^{2} to get 108b^{2}.

$$\left(-162b^{3}+108b^{2}+864b\right)\left(3b+8\right)$$

Apply the distributive property by multiplying each term of -162b^{3}+108b^{2}+864b by each term of 3b+8.

$$-486b^{4}-1296b^{3}+324b^{3}+864b^{2}+2592b^{2}+6912b$$

Combine -1296b^{3} and 324b^{3} to get -972b^{3}.

$$-486b^{4}-972b^{3}+864b^{2}+2592b^{2}+6912b$$

Combine 864b^{2} and 2592b^{2} to get 3456b^{2}.

$$-486b^{4}-972b^{3}+3456b^{2}+6912b$$