Solve (x-5)(x-10)(x-6)-12-9(x-10)-(x-6)-4(x-5)

$$(x-5)(x-10)(x-6)-12-9(x-10)-(x-6)-4(x-5)$$

Evaluate

$$\left(x-7\right)\left(x^{2}-14x+28\right)$$

Solution Steps

Apply the distributive property by multiplying each term of x-5 by each term of x-10.

$$\left(x^{2}-10x-5x+50\right)\left(x-6\right)-12-9\left(x-10\right)-\left(x-6\right)-4\left(x-5\right)$$

Combine -10x and -5x to get -15x.

$$\left(x^{2}-15x+50\right)\left(x-6\right)-12-9\left(x-10\right)-\left(x-6\right)-4\left(x-5\right)$$

Apply the distributive property by multiplying each term of x^{2}-15x+50 by each term of x-6.

$$x^{3}-6x^{2}-15x^{2}+90x+50x-300-12-9\left(x-10\right)-\left(x-6\right)-4\left(x-5\right)$$

Combine -6x^{2} and -15x^{2} to get -21x^{2}.

$$x^{3}-21x^{2}+90x+50x-300-12-9\left(x-10\right)-\left(x-6\right)-4\left(x-5\right)$$

Combine 90x and 50x to get 140x.

$$x^{3}-21x^{2}+140x-300-12-9\left(x-10\right)-\left(x-6\right)-4\left(x-5\right)$$

Subtract 12 from -300 to get -312.

$$x^{3}-21x^{2}+140x-312-9\left(x-10\right)-\left(x-6\right)-4\left(x-5\right)$$

Use the distributive property to multiply -9 by x-10.

$$x^{3}-21x^{2}+140x-312-9x+90-\left(x-6\right)-4\left(x-5\right)$$

Combine 140x and -9x to get 131x.

$$x^{3}-21x^{2}+131x-312+90-\left(x-6\right)-4\left(x-5\right)$$

Add -312 and 90 to get -222.

$$x^{3}-21x^{2}+131x-222-\left(x-6\right)-4\left(x-5\right)$$

To find the opposite of x-6, find the opposite of each term.

$$x^{3}-21x^{2}+131x-222-x-\left(-6\right)-4\left(x-5\right)$$

The opposite of -6 is 6.

$$x^{3}-21x^{2}+131x-222-x+6-4\left(x-5\right)$$

Combine 131x and -x to get 130x.

$$x^{3}-21x^{2}+130x-222+6-4\left(x-5\right)$$

Add -222 and 6 to get -216.

$$x^{3}-21x^{2}+130x-216-4\left(x-5\right)$$

Use the distributive property to multiply -4 by x-5.

$$x^{3}-21x^{2}+130x-216-4x+20$$

Combine 130x and -4x to get 126x.

$$x^{3}-21x^{2}+126x-216+20$$

Add -216 and 20 to get -196.

$$x^{3}-21x^{2}+126x-196$$

Expand

$$x^{3}-21x^{2}+126x-196$$

Solution Steps

Apply the distributive property by multiplying each term of x-5 by each term of x-10.

$$\left(x^{2}-10x-5x+50\right)\left(x-6\right)-12-9\left(x-10\right)-\left(x-6\right)-4\left(x-5\right)$$

Combine -10x and -5x to get -15x.

$$\left(x^{2}-15x+50\right)\left(x-6\right)-12-9\left(x-10\right)-\left(x-6\right)-4\left(x-5\right)$$

Apply the distributive property by multiplying each term of x^{2}-15x+50 by each term of x-6.

$$x^{3}-6x^{2}-15x^{2}+90x+50x-300-12-9\left(x-10\right)-\left(x-6\right)-4\left(x-5\right)$$

Combine -6x^{2} and -15x^{2} to get -21x^{2}.

$$x^{3}-21x^{2}+90x+50x-300-12-9\left(x-10\right)-\left(x-6\right)-4\left(x-5\right)$$

Combine 90x and 50x to get 140x.

$$x^{3}-21x^{2}+140x-300-12-9\left(x-10\right)-\left(x-6\right)-4\left(x-5\right)$$

Subtract 12 from -300 to get -312.

$$x^{3}-21x^{2}+140x-312-9\left(x-10\right)-\left(x-6\right)-4\left(x-5\right)$$

Use the distributive property to multiply -9 by x-10.

$$x^{3}-21x^{2}+140x-312-9x+90-\left(x-6\right)-4\left(x-5\right)$$

Combine 140x and -9x to get 131x.

$$x^{3}-21x^{2}+131x-312+90-\left(x-6\right)-4\left(x-5\right)$$

Add -312 and 90 to get -222.

$$x^{3}-21x^{2}+131x-222-\left(x-6\right)-4\left(x-5\right)$$

To find the opposite of x-6, find the opposite of each term.

$$x^{3}-21x^{2}+131x-222-x-\left(-6\right)-4\left(x-5\right)$$

The opposite of -6 is 6.

$$x^{3}-21x^{2}+131x-222-x+6-4\left(x-5\right)$$

Combine 131x and -x to get 130x.

$$x^{3}-21x^{2}+130x-222+6-4\left(x-5\right)$$

Add -222 and 6 to get -216.

$$x^{3}-21x^{2}+130x-216-4\left(x-5\right)$$

Use the distributive property to multiply -4 by x-5.

$$x^{3}-21x^{2}+130x-216-4x+20$$

Combine 130x and -4x to get 126x.

$$x^{3}-21x^{2}+126x-216+20$$

Add -216 and 20 to get -196.

$$x^{3}-21x^{2}+126x-196$$