What is factor ((x+h)^2-2(x+h)^3)-(x^2-2x^3) ?

The solution to factor ((x+h)^2-2(x+h)^3)-(x^2-2x^3) is -h(6x^2+6xh-2x+2h^2-h)

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factor ((x+h)^2-2(x+h)^3)-(x^2-2x^3)

factor

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

- h (6 x^{2} + 6 x h - 2 x + 2 h^{2} - h)

Solution steps

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

Remove parentheses:

(a) = a

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

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

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

(x + h)^{2} : x^{2} + 2 x h + h^{2}

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

(x + h)^{3} : x^{3} + 3 x^{2} h + 3 x h^{2} + h^{3}

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

Expand

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

= x^{2} + 2 x h + h^{2} - 2 x^{3} - 6 x^{2} h - 6 x h^{2} - 2 h^{3} + x^{2} (2 x - 1)

Expand

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

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

Simplify

x^{2} + 2 x h + h^{2} - 2 x^{3} - 6 x^{2} h - 6 x h^{2} - 2 h^{3} + 2 x^{3} - x^{2} : - 6 x^{2} h - 6 x h^{2} + 2 x h - 2 h^{3} + h^{2}

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

Apply exponent rule:

a^{b + c} = a^{b} a^{c}

h^{2} = hh, h^{3} = h h^{2}, x h^{2} = hh

= - 6 x^{2} h - 6 x hh + 2 x h - 2 h h^{2} + hh

Factor out common term

- h

= - h (6 x^{2} + 6 x h - 2 x + 2 h^{2} - h)

∣ x + 3 ∣ + ∣ x - 2 ∣ = 7

\frac{3 x + 2}{x + 5} \geq 0

\frac{2}{4 x - 3} + 7 \geq 0

52 \cdot 2

What is factor ((x+h)^2-2(x+h)^3)-(x^2-2x^3) ?
The solution to factor ((x+h)^2-2(x+h)^3)-(x^2-2x^3) is -h(6x^2+6xh-2x+2h^2-h)