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Show that: sin^8A-cos^8A=(sin^2A-cos^2A)...

Show that: `sin^8A-cos^8A=(sin^2A-cos^2A)(1-2sin^2Acos^2A)`

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`(\sin ^{4} {~A})^{2}-(\cos ^{4} {~A})^{2} `
`=(\sin ^{4} {~A}+\cos ^{4} {~A})(\sin ^{4} {~A}-\cos ^{4} {~A})= `
`{[(\sin ^{2} {~A}+\cos ^{2} {~A})^{2}-2 \sin ^{2} {~A} \cos ^{2} {~A}][(\sin ^{2} {~A}-\cos ^{2} {~A})(\sin ^{2} {~A}+\cos ^{2} {~A})]} `
`=(1-2 \sin ^{2} {~A} \cos ^{2} {~A})(\sin ^{2} {~A}-\cos ^{2} {~A})`
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