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

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

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

simplify

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

x^{3} - 4 x^{2} + 4 x + 5

Solution steps

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

Expand

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

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

Expand

- (x + 2) (x - 3) : - x^{2} + x + 6

= x^{3} - 3 x^{2} + 3 x - 1 - x^{2} + x + 6

Group like terms

= x^{3} - 3 x^{2} - x^{2} + 3 x + x - 1 + 6

Add similar elements:

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

= x^{3} - 4 x^{2} + 3 x + x - 1 + 6

Add similar elements:

3 x + x = 4 x

= x^{3} - 4 x^{2} + 4 x - 1 + 6

Add the numbers:

- 1 + 6 = 5

= x^{3} - 4 x^{2} + 4 x + 5

x^{2} e^{\frac{- y ^{2}}{x ^{2}}}

5 \frac{m}{s}

(2 x + p - c)^{2} - (2 x - p + c)^{2}

aa + 30 - 10

\frac{( 42 a \cdot b ^{4} \cdot c ^{4} )}{( 21 a ^{8} \cdot b ^{2} \cdot c ^{3} )}

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