Solve y=-x(x-2)(x-3)(x-9)(x+6)

$$y = - x ( x - 2 ) ( x - 3 ) ( x - 9 ) ( x + 6 )$$

Solve for y

$$y=-x\left(x-9\right)\left(x-3\right)\left(x-2\right)\left(x+6\right)$$

Solution Steps

Use the distributive property to multiply -x by x-2.

$$y=\left(\left(-x\right)x-2\left(-x\right)\right)\left(x-3\right)\left(x-9\right)\left(x+6\right)$$

Multiply -2 and -1 to get 2.

$$y=\left(\left(-x\right)x+2x\right)\left(x-3\right)\left(x-9\right)\left(x+6\right)$$

Use the distributive property to multiply \left(-x\right)x+2x by x-3.

$$y=\left(\left(-x\right)x^{2}-3\left(-x\right)x+2x^{2}-6x\right)\left(x-9\right)\left(x+6\right)$$

Multiply -3 and -1 to get 3.

$$y=\left(\left(-x\right)x^{2}+3xx+2x^{2}-6x\right)\left(x-9\right)\left(x+6\right)$$

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

$$y=\left(\left(-x\right)x^{2}+3x^{2}+2x^{2}-6x\right)\left(x-9\right)\left(x+6\right)$$

Combine 3x^{2} and 2x^{2} to get 5x^{2}.

$$y=\left(\left(-x\right)x^{2}+5x^{2}-6x\right)\left(x-9\right)\left(x+6\right)$$

Use the distributive property to multiply \left(-x\right)x^{2}+5x^{2}-6x by x-9 and combine like terms.

$$y=\left(\left(-x\right)x^{3}-9\left(-x\right)x^{2}+5x^{3}-51x^{2}+54x\right)\left(x+6\right)$$

Multiply -9 and -1 to get 9.

$$y=\left(\left(-x\right)x^{3}+9xx^{2}+5x^{3}-51x^{2}+54x\right)\left(x+6\right)$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$y=\left(\left(-x\right)x^{3}+9x^{3}+5x^{3}-51x^{2}+54x\right)\left(x+6\right)$$

Combine 9x^{3} and 5x^{3} to get 14x^{3}.

$$y=\left(\left(-x\right)x^{3}+14x^{3}-51x^{2}+54x\right)\left(x+6\right)$$

Use the distributive property to multiply \left(-x\right)x^{3}+14x^{3}-51x^{2}+54x by x+6 and combine like terms.

$$y=\left(-x\right)x^{4}+6\left(-x\right)x^{3}+14x^{4}+33x^{3}-252x^{2}+324x$$

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$y=-x^{5}+6\left(-1\right)xx^{3}+14x^{4}+33x^{3}-252x^{2}+324x$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$y=-x^{5}+6\left(-1\right)x^{4}+14x^{4}+33x^{3}-252x^{2}+324x$$

Multiply 6 and -1 to get -6.

$$y=-x^{5}-6x^{4}+14x^{4}+33x^{3}-252x^{2}+324x$$

Combine -6x^{4} and 14x^{4} to get 8x^{4}.

$$y=-x^{5}+8x^{4}+33x^{3}-252x^{2}+324x$$