Solve y=(3x^4-x+1)(-x^5+5)

$$y = ( 3 x ^ { 4 } - x + 1 ) ( - x ^ { 5 } + 5 )$$

Solve for y

$$y=\left(3x^{4}-x+1\right)\left(5-x^{5}\right)$$

Solution Steps

Use the distributive property to multiply 3x^{4}-x+1 by -x^{5}+5.

$$y=3x^{4}\left(-x^{5}\right)+15x^{4}-x\left(-x^{5}\right)-5x-x^{5}+5$$

Multiply -1 and -1 to get 1.

$$y=3x^{4}\left(-x^{5}\right)+15x^{4}+xx^{5}-5x-x^{5}+5$$

To multiply powers of the same base, add their exponents. Add 1 and 5 to get 6.

$$y=3x^{4}\left(-x^{5}\right)+15x^{4}+x^{6}-5x-x^{5}+5$$

To multiply powers of the same base, add their exponents. Add 4 and 5 to get 9.

$$y=3x^{9}\left(-1\right)+15x^{4}+x^{6}-5x-x^{5}+5$$

Multiply 3 and -1 to get -3.

$$y=-3x^{9}+15x^{4}+x^{6}-5x-x^{5}+5$$