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

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

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

expand

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

x^{3} 2 x + 1 - 2 x^{2} 2 x + 1 + x 2 x + 1

Solution steps

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

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

Apply FOIL method

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

= 2 x + 1 (x^{3} - 2 x^{2} + x)

Apply the distributive law:

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

2 x + 1 (x^{3} - 2 x^{2} + x) = 2 x + 1 x^{3} + 2 x + 1 (- 2 x^{2}) + 2 x + 1 x

= 2 x + 1 x^{3} + 2 x + 1 (- 2 x^{2}) + 2 x + 1 x

Simplify

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

= x^{3} 2 x + 1 - 2 x^{2} 2 x + 1 + x 2 x + 1

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

(4 a^{2} ma s^{2} ab, 5 b) ma s (6 a^{2} - 7 ab)

(v + Δ v)^{3}

\frac{6 x ^{2} - 3 x + 36}{x ( x ^{2} + 9 )}

(x^{3} - \frac{2}{x ^{2}})^{10}

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