What is x(ax-1)(ax-a-1)(x+1)+a ?

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

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simplify x(ax-1)(ax-a-1)(x+1)+a

simplify

x (a x - 1) (a x - a - 1) (x + 1) + a

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

Solution steps

x (a x - 1) (a x - a - 1) (x + 1) + a

Apply FOIL method

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

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

Expand

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

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

Distribute parentheses

= x a^{2} x^{3} + x (- 2 a x^{2}) + x (- x a^{2}) + xx + x (- a x) + x a + x \cdot 1 + a

Simplify

x a^{2} x^{3} + x (- 2 a x^{2}) + x (- x a^{2}) + xx + x (- a x) + x a + x \cdot 1 : x^{4} a^{2} - 2 a x^{3} - x^{2} a^{2} + x^{2} - a x^{2} + a x + x

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

2 ab + 3 ab + ab

x^{2} x^{3}

(9 x^{2} + 4 x) - (- 4 x^{2} - 7)

\frac{3}{5} \cdot \frac{4}{7}

(x + 1) (1 - x)

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