Solve 3(x+5)(x-3)(x-5)(x-4)

$$3 ( x + 5 ) ( x - 3 ) ( x - 5 ) ( x - 4 )$$

Evaluate

$$3\left(x-4\right)\left(x-3\right)\left(x^{2}-25\right)$$

Solution Steps

Use the distributive property to multiply 3 by x+5.

$$\left(3x+15\right)\left(x-3\right)\left(x-5\right)\left(x-4\right)$$

Apply the distributive property by multiplying each term of 3x+15 by each term of x-3.

$$\left(3x^{2}-9x+15x-45\right)\left(x-5\right)\left(x-4\right)$$

Combine -9x and 15x to get 6x.

$$\left(3x^{2}+6x-45\right)\left(x-5\right)\left(x-4\right)$$

Apply the distributive property by multiplying each term of 3x^{2}+6x-45 by each term of x-5.

$$\left(3x^{3}-15x^{2}+6x^{2}-30x-45x+225\right)\left(x-4\right)$$

Combine -15x^{2} and 6x^{2} to get -9x^{2}.

$$\left(3x^{3}-9x^{2}-30x-45x+225\right)\left(x-4\right)$$

Combine -30x and -45x to get -75x.

$$\left(3x^{3}-9x^{2}-75x+225\right)\left(x-4\right)$$

Apply the distributive property by multiplying each term of 3x^{3}-9x^{2}-75x+225 by each term of x-4.

$$3x^{4}-12x^{3}-9x^{3}+36x^{2}-75x^{2}+300x+225x-900$$

Combine -12x^{3} and -9x^{3} to get -21x^{3}.

$$3x^{4}-21x^{3}+36x^{2}-75x^{2}+300x+225x-900$$

Combine 36x^{2} and -75x^{2} to get -39x^{2}.

$$3x^{4}-21x^{3}-39x^{2}+300x+225x-900$$

Combine 300x and 225x to get 525x.

$$3x^{4}-21x^{3}-39x^{2}+525x-900$$

Expand

$$3x^{4}-21x^{3}-39x^{2}+525x-900$$

Solution Steps

Use the distributive property to multiply 3 by x+5.

$$\left(3x+15\right)\left(x-3\right)\left(x-5\right)\left(x-4\right)$$

Apply the distributive property by multiplying each term of 3x+15 by each term of x-3.

$$\left(3x^{2}-9x+15x-45\right)\left(x-5\right)\left(x-4\right)$$

Combine -9x and 15x to get 6x.

$$\left(3x^{2}+6x-45\right)\left(x-5\right)\left(x-4\right)$$

Apply the distributive property by multiplying each term of 3x^{2}+6x-45 by each term of x-5.

$$\left(3x^{3}-15x^{2}+6x^{2}-30x-45x+225\right)\left(x-4\right)$$

Combine -15x^{2} and 6x^{2} to get -9x^{2}.

$$\left(3x^{3}-9x^{2}-30x-45x+225\right)\left(x-4\right)$$

Combine -30x and -45x to get -75x.

$$\left(3x^{3}-9x^{2}-75x+225\right)\left(x-4\right)$$

Apply the distributive property by multiplying each term of 3x^{3}-9x^{2}-75x+225 by each term of x-4.

$$3x^{4}-12x^{3}-9x^{3}+36x^{2}-75x^{2}+300x+225x-900$$

Combine -12x^{3} and -9x^{3} to get -21x^{3}.

$$3x^{4}-21x^{3}+36x^{2}-75x^{2}+300x+225x-900$$

Combine 36x^{2} and -75x^{2} to get -39x^{2}.

$$3x^{4}-21x^{3}-39x^{2}+300x+225x-900$$

Combine 300x and 225x to get 525x.

$$3x^{4}-21x^{3}-39x^{2}+525x-900$$