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

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

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

expand

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

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

Solution steps

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

Expand

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

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

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

Apply the distributive law:

m (a + b + c) = ma + mb + m c

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

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

Simplify

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

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

P (- 1, 2) Q (4, - 5)

\frac{1 + x ^{2}}{1 + x}

(2 x - \frac{1}{2} y)^{5}

\frac{16 s}{( s ^{2} + 1 ) ^{2} ( s ^{2} + 4 )}

\frac{v + 6}{( v + 8 ) ( v - 4 )}

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