Solve 32(x+6)(x)(x-3)(x-1)

$$32 ( x + 6 ) ( x ) ( x - 3 ) ( x - 1 )$$

Evaluate

$$32x\left(x-3\right)\left(x-1\right)\left(x+6\right)$$

Solution Steps

Use the distributive property to multiply 32 by x+6.

$$\left(32x+192\right)x\left(x-3\right)\left(x-1\right)$$

Use the distributive property to multiply 32x+192 by x.

$$\left(32x^{2}+192x\right)\left(x-3\right)\left(x-1\right)$$

Apply the distributive property by multiplying each term of 32x^{2}+192x by each term of x-3.

$$\left(32x^{3}-96x^{2}+192x^{2}-576x\right)\left(x-1\right)$$

Combine -96x^{2} and 192x^{2} to get 96x^{2}.

$$\left(32x^{3}+96x^{2}-576x\right)\left(x-1\right)$$

Apply the distributive property by multiplying each term of 32x^{3}+96x^{2}-576x by each term of x-1.

$$32x^{4}-32x^{3}+96x^{3}-96x^{2}-576x^{2}+576x$$

Combine -32x^{3} and 96x^{3} to get 64x^{3}.

$$32x^{4}+64x^{3}-96x^{2}-576x^{2}+576x$$

Combine -96x^{2} and -576x^{2} to get -672x^{2}.

$$32x^{4}+64x^{3}-672x^{2}+576x$$

Expand

$$32x^{4}+64x^{3}-672x^{2}+576x$$

Solution Steps

Use the distributive property to multiply 32 by x+6.

$$\left(32x+192\right)x\left(x-3\right)\left(x-1\right)$$

Use the distributive property to multiply 32x+192 by x.

$$\left(32x^{2}+192x\right)\left(x-3\right)\left(x-1\right)$$

Apply the distributive property by multiplying each term of 32x^{2}+192x by each term of x-3.

$$\left(32x^{3}-96x^{2}+192x^{2}-576x\right)\left(x-1\right)$$

Combine -96x^{2} and 192x^{2} to get 96x^{2}.

$$\left(32x^{3}+96x^{2}-576x\right)\left(x-1\right)$$

Apply the distributive property by multiplying each term of 32x^{3}+96x^{2}-576x by each term of x-1.

$$32x^{4}-32x^{3}+96x^{3}-96x^{2}-576x^{2}+576x$$

Combine -32x^{3} and 96x^{3} to get 64x^{3}.

$$32x^{4}+64x^{3}-96x^{2}-576x^{2}+576x$$

Combine -96x^{2} and -576x^{2} to get -672x^{2}.

$$32x^{4}+64x^{3}-672x^{2}+576x$$