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

The solution to (x^2+4x+8)^2-3x(x^2+4x+8)+2x^2 is x^4+5x^3+22x^2+40x+64

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

simplify

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

x^{4} + 5 x^{3} + 22 x^{2} + 40 x + 64

Solution steps

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

Expand

(x^{2} + 4 x + 8)^{2} : x^{4} + 8 x^{3} + 32 x^{2} + 64 x + 64

= x^{4} + 8 x^{3} + 32 x^{2} + 64 x + 64 - 3 x (x^{2} + 4 x + 8) + 2 x^{2}

Expand

- 3 x (x^{2} + 4 x + 8) : - 3 x^{3} - 12 x^{2} - 24 x

= x^{4} + 8 x^{3} + 32 x^{2} + 64 x + 64 - 3 x^{3} - 12 x^{2} - 24 x + 2 x^{2}

Group like terms

= x^{4} + 8 x^{3} - 3 x^{3} + 32 x^{2} - 12 x^{2} + 2 x^{2} + 64 x - 24 x + 64

Add similar elements:

8 x^{3} - 3 x^{3} = 5 x^{3}

= x^{4} + 5 x^{3} + 32 x^{2} - 12 x^{2} + 2 x^{2} + 64 x - 24 x + 64

Add similar elements:

32 x^{2} - 12 x^{2} + 2 x^{2} = 22 x^{2}

= x^{4} + 5 x^{3} + 22 x^{2} + 64 x - 24 x + 64

Add similar elements:

64 x - 24 x = 40 x

= x^{4} + 5 x^{3} + 22 x^{2} + 40 x + 64

16 x y^{3} - 64 x y

\frac{( 3 - x )}{( 4 x - 12 )}

(\frac{3 x + 1}{3 x})^{3}

(10 x^{2})^{2}

(x + h + 1) \cdot (x + h - 1)

What is (x^2+4x+8)^2-3x(x^2+4x+8)+2x^2 ?
The solution to (x^2+4x+8)^2-3x(x^2+4x+8)+2x^2 is x^4+5x^3+22x^2+40x+64