What is 4x(-5x^2+3x-2)+(x^2-3x+1)(x^2-3) ?

The solution to 4x(-5x^2+3x-2)+(x^2-3x+1)(x^2-3) is x^4-23x^3+10x^2+x-3

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simplify 4x(-5x^2+3x-2)+(x^2-3x+1)(x^2-3)

simplify

4 x (- 5 x^{2} + 3 x - 2) + (x^{2} - 3 x + 1) (x^{2} - 3)

x^{4} - 23 x^{3} + 10 x^{2} + x - 3

Solution steps

4 x (- 5 x^{2} + 3 x - 2) + (x^{2} - 3 x + 1) (x^{2} - 3)

Expand

4 x (- 5 x^{2} + 3 x - 2) : - 20 x^{3} + 12 x^{2} - 8 x

= - 20 x^{3} + 12 x^{2} - 8 x + (x^{2} - 3 x + 1) (x^{2} - 3)

Expand

(x^{2} - 3 x + 1) (x^{2} - 3) : x^{4} - 3 x^{3} - 2 x^{2} + 9 x - 3

= - 20 x^{3} + 12 x^{2} - 8 x + x^{4} - 3 x^{3} - 2 x^{2} + 9 x - 3

Group like terms

= x^{4} - 20 x^{3} - 3 x^{3} + 12 x^{2} - 2 x^{2} - 8 x + 9 x - 3

Add similar elements:

- 20 x^{3} - 3 x^{3} = - 23 x^{3}

= x^{4} - 23 x^{3} + 12 x^{2} - 2 x^{2} - 8 x + 9 x - 3

Add similar elements:

12 x^{2} - 2 x^{2} = 10 x^{2}

= x^{4} - 23 x^{3} + 10 x^{2} - 8 x + 9 x - 3

Add similar elements:

- 8 x + 9 x = x

= x^{4} - 23 x^{3} + 10 x^{2} + x - 3

- 11 \times 1

5 \times (- 4) 20

- \frac{2}{3} \times 9

(y^{2} - y + 1)^{2}

What is 4x(-5x^2+3x-2)+(x^2-3x+1)(x^2-3) ?
The solution to 4x(-5x^2+3x-2)+(x^2-3x+1)(x^2-3) is x^4-23x^3+10x^2+x-3