What is (2x-3)^3+(8x+1)(4-x^2)-(x+2)^2 ?

The solution to (2x-3)^3+(8x+1)(4-x^2)-(x+2)^2 is -38x^2+82x-27

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simplify (2x-3)^3+(8x+1)(4-x^2)-(x+2)^2

simplify

(2 x - 3)^{3} + (8 x + 1) (4 - x^{2}) - (x + 2)^{2}

- 38 x^{2} + 82 x - 27

Solution steps

(2 x - 3)^{3} + (8 x + 1) (4 - x^{2}) - (x + 2)^{2}

Expand

(2 x - 3)^{3} : 8 x^{3} - 36 x^{2} + 54 x - 27

= 8 x^{3} - 36 x^{2} + 54 x - 27 + (8 x + 1) (4 - x^{2}) - (x + 2)^{2}

Expand

(8 x + 1) (4 - x^{2}) : 32 x - 8 x^{3} + 4 - x^{2}

= 8 x^{3} - 36 x^{2} + 54 x - 27 + 32 x - 8 x^{3} + 4 - x^{2} - (x + 2)^{2}

Expand

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

= 8 x^{3} - 36 x^{2} + 54 x - 27 + 32 x - 8 x^{3} + 4 - x^{2} - x^{2} - 4 x - 4

Group like terms

= 8 x^{3} - 8 x^{3} - 36 x^{2} - x^{2} - x^{2} + 54 x + 32 x - 4 x - 27 + 4 - 4

Add similar elements:

8 x^{3} - 8 x^{3} = 0

= - 36 x^{2} - x^{2} - x^{2} + 54 x + 32 x - 4 x - 27 + 4 - 4

Add similar elements:

- 36 x^{2} - x^{2} - x^{2} = - 38 x^{2}

= - 38 x^{2} + 54 x + 32 x - 4 x - 27 + 4 - 4

Add similar elements:

54 x + 32 x - 4 x = 82 x

= - 38 x^{2} + 82 x - 27 + 4 - 4

Add the numbers:

- 27 + 4 - 4 = - 27

= - 38 x^{2} + 82 x - 27

(2 x + 3 y - 5) (x - y + 3)

\frac{( x _{1} + x _{2} )}{( x _{1} \cdot x _{2} )}

(2 a + 3 b)^{3} - (2 a - 3 b)^{3}

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

m^{4} - 5 m^{2} n - 14 n^{2}

What is (2x-3)^3+(8x+1)(4-x^2)-(x+2)^2 ?
The solution to (2x-3)^3+(8x+1)(4-x^2)-(x+2)^2 is -38x^2+82x-27