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

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

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

expand

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

\frac{4 x ^{3} - 3 x + 4 2 x ^{2} + 4 2 x + 2 - 1}{4}

Solution steps

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

Expand

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

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

Apply the distributive law:

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

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

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

Simplify

\frac{4 x ^{2} + 4 x + 1}{4} x + \frac{4 x ^{2} + 4 x + 1}{4} (- 1) + \frac{4 x ^{2} + 4 x + 1}{4} 2 : \frac{4 x ^{3} - 3 x + 4 2 x ^{2} + 4 2 x + 2 - 1}{4}

= \frac{4 x ^{3} - 3 x + 4 2 x ^{2} + 4 2 x + 2 - 1}{4}

e (k t + c)

(x - 2) d x

\frac{s ^{2} ( s + 3 )}{5 s ^{3} + 17 s ^{2} + 9 s + 6}

\frac{62.41}{s ( s ^{2} + 62.41 )}

(\frac{x}{3} + 10)^{5}

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