What is (x+1)^2(x-2)+(x+1)(x-2)^2 ?

The solution to (x+1)^2(x-2)+(x+1)(x-2)^2 is 2x^3-3x^2-3x+2

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simplify (x+1)^2(x-2)+(x+1)(x-2)^2

simplify

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

2 x^{3} - 3 x^{2} - 3 x + 2

Solution steps

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

= (x + 1)^{2} (x - 2) + (x - 2)^{2} (x + 1)

Expand

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

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

Expand

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

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

Group like terms

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

Add similar elements:

x^{3} + x^{3} = 2 x^{3}

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

Add the numbers:

- 2 + 4 = 2

= 2 x^{3} - 3 x^{2} - 3 x + 2

(6^{- 1})^{2}

3 (7 p - 3 q + 9)

\frac{x ^{2} + 7 x + 6}{x ^{2} - 5 x - 6}

(- 2) (- 2) (- 2) (- 2)

11 - (- 1)

What is (x+1)^2(x-2)+(x+1)(x-2)^2 ?
The solution to (x+1)^2(x-2)+(x+1)(x-2)^2 is 2x^3-3x^2-3x+2