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

The solution to (x-1)(x+2)^2-(x-1)^2(x+2) is 3x^2+3x-6

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

simplify

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

3 x^{2} + 3 x - 6

Solution steps

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

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

Expand

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

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

Expand

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

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

Group like terms

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

Add similar elements:

x^{3} - x^{3} = 0

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

Subtract the numbers:

- 4 - 2 = - 6

= 3 x^{2} + 3 x - 6

5 (- 9 q + 7) + 3 (5 q + 5)

\frac{a b ^{2} ( 3 a ^{2} b ) ^{2}}{3 a}

6 m - 2 (- 3 m + 8)

27 - 33

\frac{15}{10 - 3}

What is (x-1)(x+2)^2-(x-1)^2(x+2) ?
The solution to (x-1)(x+2)^2-(x-1)^2(x+2) is 3x^2+3x-6