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

The solution to expand (-x^2+2x+4)^2 is x^4-4x^3-4x^2+16x+16

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

expand

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

x^{4} - 4 x^{3} - 4 x^{2} + 16 x + 16

Solution steps

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

Apply exponent rule:

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

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

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

Distribute parentheses

= - x^{2} (- x^{2}) - x^{2} \cdot 2 x - x^{2} \cdot 4 + 2 x (- x^{2}) + 2 x \cdot 2 x + 2 x \cdot 4 + 4 (- x^{2}) + 4 \cdot 2 x + 4 \cdot 4

Simplify

- x^{2} (- x^{2}) - x^{2} \cdot 2 x - x^{2} \cdot 4 + 2 x (- x^{2}) + 2 x \cdot 2 x + 2 x \cdot 4 + 4 (- x^{2}) + 4 \cdot 2 x + 4 \cdot 4 : x^{4} - 4 x^{3} - 4 x^{2} + 16 x + 16

= x^{4} - 4 x^{3} - 4 x^{2} + 16 x + 16

- 3 - 17

\frac{150}{8}

\frac{- 3}{2}

- 4 + 35

- 2 i + i

What is expand (-x^2+2x+4)^2 ?
The solution to expand (-x^2+2x+4)^2 is x^4-4x^3-4x^2+16x+16