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

The solution to expand (-x^2+4x+2)^2 is x^4-8x^3+12x^2+16x+4

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

expand

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

x^{4} - 8 x^{3} + 12 x^{2} + 16 x + 4

Solution steps

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

Apply exponent rule:

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

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

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

Distribute parentheses

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

Simplify

- x^{2} (- x^{2}) - x^{2} \cdot 4 x - x^{2} \cdot 2 + 4 x (- x^{2}) + 4 x \cdot 4 x + 4 x \cdot 2 + 2 (- x^{2}) + 2 \cdot 4 x + 2 \cdot 2 : x^{4} - 8 x^{3} + 12 x^{2} + 16 x + 4

= x^{4} - 8 x^{3} + 12 x^{2} + 16 x + 4

- x (7 x - 8)

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

3 (12 - \frac{1}{3} (12 + x))

10 lo g_{10} (1000)

\frac{sin ( t )}{cos ( t )}

What is expand (-x^2+4x+2)^2 ?
The solution to expand (-x^2+4x+2)^2 is x^4-8x^3+12x^2+16x+4