What is expand (-xsin^2(y)-xcos^2(y))^2 ?

The solution to expand (-xsin^2(y)-xcos^2(y))^2 is x^2sin^4(y)+2x^2sin^2(y)cos^2(y)+x^2cos^4(y)

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expand (-xsin^2(y)-xcos^2(y))^2

expand

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

x^{2} sin^{4} (y) + 2 x^{2} sin^{2} (y) cos^{2} (y) + x^{2} cos^{4} (y)

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

= x^{2} sin^{4} (y) + 2 x^{2} sin^{2} (y) cos^{2} (y) + x^{2} cos^{4} (y)

(cos (x) - cot (x))^{2}

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

(\frac{1}{6} x^{2} + \frac{5}{6})^{3}

1 - cos (b) (1 + cos (b))

What is expand (-xsin^2(y)-xcos^2(y))^2 ?
The solution to expand (-xsin^2(y)-xcos^2(y))^2 is x^2sin^4(y)+2x^2sin^2(y)cos^2(y)+x^2cos^4(y)