What is expand x^3(sin(y)-x)^2 ?

The solution to expand x^3(sin(y)-x)^2 is x^3sin^2(y)-2x^4sin(y)+x^5

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expand x^3(sin(y)-x)^2

expand

x^{3} (sin (y) - x)^{2}

x^{3} sin^{2} (y) - 2 x^{4} sin (y) + x^{5}

Solution steps

x^{3} (sin (y) - x)^{2}

Expand

(sin (y) - x)^{2} : sin^{2} (y) - 2 x sin (y) + x^{2}

= x^{3} (sin^{2} (y) - 2 x sin (y) + x^{2})

Apply the distributive law:

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

x^{3} (sin^{2} (y) - 2 x sin (y) + x^{2}) = x^{3} sin^{2} (y) + x^{3} (- 2 x sin (y)) + x^{3} x^{2}

= x^{3} sin^{2} (y) + x^{3} (- 2 x sin (y)) + x^{3} x^{2}

Simplify

x^{3} sin^{2} (y) + x^{3} (- 2 x sin (y)) + x^{3} x^{2} : x^{3} sin^{2} (y) - 2 x^{4} sin (y) + x^{5}

= x^{3} sin^{2} (y) - 2 x^{4} sin (y) + x^{5}

\frac{( 2 \cdot s ^{2} + 6 \cdot s + 5 )}{( s + 1 ) ^{2} \cdot ( s + 2 )}

\frac{30 x ^{2}}{( 1 + x ^{2} ) ^{2}}

3 (- 0.4 e^{- 0.4 x} + 0.6 e^{- 0.6 x})

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

(2 x + 1) (2 x + 2Δ x - 1)

What is expand x^3(sin(y)-x)^2 ?
The solution to expand x^3(sin(y)-x)^2 is x^3sin^2(y)-2x^4sin(y)+x^5