What is expand (sin(x)+xcos(x))^2 ?

The solution to expand (sin(x)+xcos(x))^2 is x^2cos^2(x)+xsin(2x)+sin^2(x)

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expand (sin(x)+xcos(x))^2

expand

(sin (x) + x cos (x))^{2}

x^{2} cos^{2} (x) + x sin (2 x) + sin^{2} (x)

Solution steps

(sin (x) + x cos (x))^{2}

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

(sin (x) + x cos (x))^{2} = sin^{2} (x) + 2 sin (x) x cos (x) + (x cos (x))^{2}

= sin^{2} (x) + 2 sin (x) x cos (x) + (x cos (x))^{2}

Simplify

sin^{2} (x) + 2 sin (x) x cos (x) + (x cos (x))^{2} : x^{2} cos^{2} (x) + x sin (2 x) + sin^{2} (x)

= x^{2} cos^{2} (x) + x sin (2 x) + sin^{2} (x)

\frac{d ^{2}}{d x ^{2}} (x^{4}) - 2 x (6 x - x^{2})

\frac{6 x ^{2} - 9 x + 1}{( x - 1 ) ^{2} ( x + 1 )}

(x - 5) (x + 5)

7 (π - 5)

(x + y)^{2}

What is expand (sin(x)+xcos(x))^2 ?
The solution to expand (sin(x)+xcos(x))^2 is x^2cos^2(x)+xsin(2x)+sin^2(x)