Question

Simplify:

sin ^ 4 A + ( 2 sin ^ 2 A ) ( cos ^ 2 A ) + cos ^ 4 A

Answer 1

i think its 3 ( sin ^ 2 A) (cos ^ 2 A)

but don't know if its right

Answer 2

Sin^4 + Cos^4 = (Sin^2 +Cos^2)^2 - 2 Sin^2Cos^2 = 1 - 2 Sin^2Cos^2

Can u do the rest?

Answer 3

\[\sin^4a+3\sin^2a*\cos^2a+\cos^4a\]
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remember:
\[\sin^2x+\cos^2x=1 => (\sin^2x+\cos^2x)^2=1^2=1\]
so this means we have:
\[(\sin^2x)^2+2sin^2x*cos^2x+(\cos^2x)^2=\sin^4x+2sin^2x*cos^2x+\cos^4x=1\]
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\[\sin^4a+2\sin^2acos^2a+\cos^4x+\sin^2a*\cos^2a\]
\[=1+\sin^2a*\cos^2a\]