Solve (x-2)(x-4)+(x-4)(x-6)+(x-6)(x-8)

$$( x - 2 ) ( x - 4 ) + ( x - 4 ) ( x - 6 ) + ( x - 6 ) ( x - 8 )$$

Evaluate

$$3x^{2}-30x+80$$

Solution Steps

Apply the distributive property by multiplying each term of x-2 by each term of x-4.

$$x^{2}-4x-2x+8+\left(x-4\right)\left(x-6\right)+\left(x-6\right)\left(x-8\right)$$

Combine -4x and -2x to get -6x.

$$x^{2}-6x+8+\left(x-4\right)\left(x-6\right)+\left(x-6\right)\left(x-8\right)$$

Apply the distributive property by multiplying each term of x-4 by each term of x-6.

$$x^{2}-6x+8+x^{2}-6x-4x+24+\left(x-6\right)\left(x-8\right)$$

Combine -6x and -4x to get -10x.

$$x^{2}-6x+8+x^{2}-10x+24+\left(x-6\right)\left(x-8\right)$$

Combine x^{2} and x^{2} to get 2x^{2}.

$$2x^{2}-6x+8-10x+24+\left(x-6\right)\left(x-8\right)$$

Combine -6x and -10x to get -16x.

$$2x^{2}-16x+8+24+\left(x-6\right)\left(x-8\right)$$

Add 8 and 24 to get 32.

$$2x^{2}-16x+32+\left(x-6\right)\left(x-8\right)$$

Apply the distributive property by multiplying each term of x-6 by each term of x-8.

$$2x^{2}-16x+32+x^{2}-8x-6x+48$$

Combine -8x and -6x to get -14x.

$$2x^{2}-16x+32+x^{2}-14x+48$$

Combine 2x^{2} and x^{2} to get 3x^{2}.

$$3x^{2}-16x+32-14x+48$$

Combine -16x and -14x to get -30x.

$$3x^{2}-30x+32+48$$

Add 32 and 48 to get 80.

$$3x^{2}-30x+80$$

Expand

$$3x^{2}-30x+80$$

Solution Steps

Apply the distributive property by multiplying each term of x-2 by each term of x-4.

$$x^{2}-4x-2x+8+\left(x-4\right)\left(x-6\right)+\left(x-6\right)\left(x-8\right)$$

Combine -4x and -2x to get -6x.

$$x^{2}-6x+8+\left(x-4\right)\left(x-6\right)+\left(x-6\right)\left(x-8\right)$$

Apply the distributive property by multiplying each term of x-4 by each term of x-6.

$$x^{2}-6x+8+x^{2}-6x-4x+24+\left(x-6\right)\left(x-8\right)$$

Combine -6x and -4x to get -10x.

$$x^{2}-6x+8+x^{2}-10x+24+\left(x-6\right)\left(x-8\right)$$

Combine x^{2} and x^{2} to get 2x^{2}.

$$2x^{2}-6x+8-10x+24+\left(x-6\right)\left(x-8\right)$$

Combine -6x and -10x to get -16x.

$$2x^{2}-16x+8+24+\left(x-6\right)\left(x-8\right)$$

Add 8 and 24 to get 32.

$$2x^{2}-16x+32+\left(x-6\right)\left(x-8\right)$$

Apply the distributive property by multiplying each term of x-6 by each term of x-8.

$$2x^{2}-16x+32+x^{2}-8x-6x+48$$

Combine -8x and -6x to get -14x.

$$2x^{2}-16x+32+x^{2}-14x+48$$

Combine 2x^{2} and x^{2} to get 3x^{2}.

$$3x^{2}-16x+32-14x+48$$

Combine -16x and -14x to get -30x.

$$3x^{2}-30x+32+48$$

Add 32 and 48 to get 80.

$$3x^{2}-30x+80$$