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

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

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expand (x+4)(x+1)(x-1)^2

expand

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

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

Solution steps

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

= (x - 1)^{2} (x + 4) (x + 1)

Expand

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

= (x^{2} - 2 x + 1) (x + 4) (x + 1)

Apply FOIL method

(x + 4) (x + 1) : x^{2} + 5 x + 4

= (x^{2} - 2 x + 1) (x^{2} + 5 x + 4)

Distribute parentheses

= x^{2} x^{2} + x^{2} \cdot 5 x + x^{2} \cdot 4 - 2 x x^{2} - 2 x \cdot 5 x - 2 x \cdot 4 + 1 \cdot x^{2} + 1 \cdot 5 x + 1 \cdot 4

Simplify

x^{2} x^{2} + x^{2} \cdot 5 x + x^{2} \cdot 4 - 2 x x^{2} - 2 x \cdot 5 x - 2 x \cdot 4 + 1 \cdot x^{2} + 1 \cdot 5 x + 1 \cdot 4 : x^{4} + 3 x^{3} - 5 x^{2} - 3 x + 4

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

2 π

- 2 e^{0}

12 + 48 - 27

(3 x^{4} - 3 x) - (3 x - 3 x^{4})

\frac{6}{48}

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